Dodawanie i odejmowanie ułamków o różnych mianownikach

Ta lekcja poświęcona jest zadaniom związanym z dodawaniem i odejmowaniem ułamków o różnych mianownikach. Jeżeli chcesz sobie przypomnieć podstawowe wiadomości dotyczące działań na ułamkach, zajrzyj do lekcji Działania na ułamkach zwykłychDjDS6URPJDziałania na ułamkach zwykłych.

Dodawanie ułamków o różnych mianownikach

Polecenie 1

Zapoznaj się z poniższym filmem.

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Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

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Ćwiczenie 1

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

W poprzednim zadaniu składniki każdej sumy były sobie równe. Nie trudno dodać równe liczby. Teraz nauczymy się dodawać różne ułamki o różnych mianownikach.

Ważne!

Aby dodać ułamki o różnych mianownikach, trzeba najpierw sprowadzić je do wspólnego mianownika, skracając lub rozszerzając. Następnie należy dodać je tak, jak się dodaje ułamki o jednakowych mianownikach.

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Ćwiczenie 2

Poniżej przedstawiono pewne wyrażenia oraz ich rozwiązania. Połącz w pary początki równości z ich zakończeniami.

\frac{1}{2} + \frac{3}{4} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{1}{3} + \frac{5}{6} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{3}{5} + \frac{3}{4} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{5}{6} + \frac{8}{9} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{5}{7} + \frac{4}{5} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{7}{8} + \frac{7}{11} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{7}{10} + \frac{8}{9} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

\frac{7}{5} + \frac{5}{12} =

Możliwe odpowiedzi: 1.

= \frac{25}{35} + \frac{28}{35} = \frac{53}{35} = 1 \frac{18}{35}

, 2.

= \frac{15}{18} + \frac{16}{18} = \frac{31}{18} = 1 \frac{13}{18}

, 3.

= \frac{12}{20} + \frac{15}{20} = \frac{27}{20} = 1 \frac{7}{20}

, 4.

= \frac{2}{6} + \frac{5}{6} = \frac{7}{6} = 1 \frac{1}{6}

, 5.

= \frac{84}{60} + \frac{25}{60} = \frac{109}{60} = 1 \frac{49}{60}

, 6.

= \frac{63}{90} + \frac{80}{90} = \frac{143}{90} = 1 \frac{53}{90}

, 7.

= \frac{77}{88} + \frac{56}{88} = \frac{133}{88} = 1 \frac{45}{88}

, 8.

= \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

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Ćwiczenie 3

Uzupełnij luki odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

1 \frac{1}{2} + \frac{5}{8} = 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 2

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

1 \frac{1}{3} + 2 \frac{4}{5} = 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 2

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 3

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 4

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

4 \frac{2}{3} + 1 \frac{3}{8} = 4

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 5

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 6

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

6 \frac{5}{7} + 3 \frac{2}{3} = 6

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 3

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 9

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 10

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

5 \frac{4}{5} + 2 \frac{6}{7} = 5

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 2

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 7

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 8

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

6 \frac{5}{8} + 1 \frac{3}{5} = 6

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 7

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 8

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

7 \frac{7}{8} + 1 \frac{5}{6} = 7

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 8

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 9

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

10 \frac{5}{7} + 3 \frac{7}{9} = 10

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 3

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 13

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 14

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

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1 \frac{1}{2} + \frac{5}{8} = 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 2

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

1 \frac{1}{3} + 2 \frac{4}{5} = 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 2

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 3

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 4

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

4 \frac{2}{3} + 1 \frac{3}{8} = 4

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 5

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 6

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

6 \frac{5}{7} + 3 \frac{2}{3} = 6

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 3

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 9

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 10

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

5 \frac{4}{5} + 2 \frac{6}{7} = 5

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 2

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 7

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 8

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

6 \frac{5}{8} + 1 \frac{3}{5} = 6

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 7

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 8

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

7 \frac{7}{8} + 1 \frac{5}{6} = 7

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 1

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 8

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 9

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

10 \frac{5}{7} + 3 \frac{7}{9} = 10

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

+ 3

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 13

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

= 14

\frac{5}{8}

, 2.

\frac{9}{40}

, 3.

\frac{28}{35}

, 4.

\frac{20}{24}

, 5.

\frac{4}{8}

, 6.

\frac{30}{35}

, 7.

\frac{49}{63}

, 8.

\frac{17}{15}

, 9.

\frac{1}{24}

, 10.

\frac{29}{21}

, 11.

\frac{5}{15}

, 12.

\frac{12}{15}

, 13.

\frac{1}{8}

, 14.

\frac{21}{24}

, 15.

\frac{9}{24}

, 16.

\frac{49}{40}

, 17.

\frac{94}{63}

, 18.

\frac{8}{21}

, 19.

\frac{25}{40}

, 20.

\frac{45}{63}

, 21.

\frac{24}{40}

, 22.

\frac{15}{21}

, 23.

\frac{9}{8}

, 24.

\frac{2}{15}

, 25.

\frac{31}{63}

, 26.

\frac{14}{21}

, 27.

\frac{17}{24}

, 28.

\frac{41}{24}

, 29.

\frac{58}{35}

, 30.

\frac{16}{24}

, 31.

\frac{23}{35}

, 32.

\frac{25}{24}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Ćwiczenie 4

Przyjrzyj się dodawanym ułamkom i wynikom dodawania.

\frac{1}{2} + \frac{1}{3} = \frac{5}{6}

\frac{1}{3} + \frac{1}{4} = \frac{7}{12}

\frac{1}{4} + \frac{1}{5} = \frac{9}{20}

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Wykonaj obliczenia tak, jak w powyższych przykładach. Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakującą liczbę dla każdej równości.

\frac{1}{5} + \frac{1}{6} =

\frac{10}{23}

, 2.

\frac{10}{21}

, 3.

\frac{11}{30}

, 4.

\frac{15}{56}

, 5.

\frac{14}{56}

, 6.

\frac{14}{45}

\frac{1}{3} + \frac{1}{7} =

\frac{10}{23}

, 2.

\frac{10}{21}

, 3.

\frac{11}{30}

, 4.

\frac{15}{56}

, 5.

\frac{14}{56}

, 6.

\frac{14}{45}

\frac{1}{9} + \frac{1}{5} =

\frac{10}{23}

, 2.

\frac{10}{21}

, 3.

\frac{11}{30}

, 4.

\frac{15}{56}

, 5.

\frac{14}{56}

, 6.

\frac{14}{45}

\frac{1}{7} + \frac{1}{8} =

\frac{10}{23}

, 2.

\frac{10}{21}

, 3.

\frac{11}{30}

, 4.

\frac{15}{56}

, 5.

\frac{14}{56}

, 6.

\frac{14}{45}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Odejmowanie ułamków o różnych mianownikach

Ważne!

Aby odjąć dwa ułamki o różnych mianownikach, trzeba najpierw sprowadzić je do wspólnego mianownika, skracając lub rozszerzając. Następnie należy odjąć je tak, jak się odejmuje ułamki o jednakowych mianownikach.

RQ66SMtCeL62Y21

Ćwiczenie 5

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakującą liczbę dla każdej równości.

\frac{1}{3} + \frac{2}{9} = \frac{5}{9}

, czyli

\frac{5}{9} - \frac{1}{3} =

\frac{3}{4}

, 2.

\frac{1}{2}

, 3.

\frac{2}{5}

, 4.

\frac{2}{9}

, 5.

\frac{2}{3}

, 6.

\frac{1}{3}

\frac{2}{5} + \frac{3}{4} = \frac{23}{20}

, czyli

1 \frac{3}{20} - \frac{3}{4} =

\frac{3}{4}

, 2.

\frac{1}{2}

, 3.

\frac{2}{5}

, 4.

\frac{2}{9}

, 5.

\frac{2}{3}

, 6.

\frac{1}{3}

\frac{1}{3} + \frac{2}{8} = \frac{14}{24}

, czyli

\frac{7}{12} - \frac{1}{4} =

\frac{3}{4}

, 2.

\frac{1}{2}

, 3.

\frac{2}{5}

, 4.

\frac{2}{9}

, 5.

\frac{2}{3}

, 6.

\frac{1}{3}

\frac{10}{22} + \frac{4}{6} = \frac{37}{33}

, czyli

1 \frac{4}{33} - \frac{5}{11} =

\frac{3}{4}

, 2.

\frac{1}{2}

, 3.

\frac{2}{5}

, 4.

\frac{2}{9}

, 5.

\frac{2}{3}

, 6.

\frac{1}{3}

Przeciągnij i upuść.

$\frac{2}{3}$ , $\frac{2}{9}$ , $\frac{1}{3}$ , $\frac{3}{4}$ , $\frac{2}{5}$ , $\frac{1}{2}$

a) $\frac{1}{3} + \frac{2}{9} = \frac{5}{9},$ czyli $\frac{5}{9} - \frac{1}{3} =$ ............
b) $\frac{2}{5} + \frac{3}{4} = \frac{23}{20},$ czyli $1 \frac{3}{20} - \frac{3}{4} =$ ............
c) $\frac{1}{3} + \frac{2}{8} = \frac{14}{24},$ czyli $\frac{7}{12} - \frac{1}{4} =$ ............
d) $\frac{10}{22} + \frac{4}{6} = \frac{37}{33},$ czyli $1 \frac{4}{33} - \frac{5}{11} =$ ............

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

RoXDaRniOlIzt2

Ćwiczenie 6

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości. 1.

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

+ \frac{2}{9} = \frac{5}{9}

, czyli

\frac{5}{9} - \frac{1}{3} =

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

\frac{1}{2} +

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

= \frac{9}{16}

, czyli

\frac{9}{16} - \frac{1}{2} =

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

+ \frac{5}{21} = \frac{15}{42}

, czyli

\frac{5}{14} - \frac{5}{21} =

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

\frac{1}{6} +

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

= \frac{7}{12}

, czyli

\frac{7}{12} - \frac{1}{6} =

\frac{5}{12}

, 2.

\frac{5}{12}

, 3.

\frac{1}{3}

, 4.

\frac{1}{16}

, 5.

\frac{5}{42}

, 6.

\frac{1}{16}

, 7.

\frac{5}{42}

, 8.

\frac{2}{9}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

RihyMSIO7E5js2

Ćwiczenie 7

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

\frac{5}{6} - \frac{9}{12} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{15}{16} - \frac{3}{4} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{19}{21} - \frac{1}{7} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{5}{6} - \frac{3}{8} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{5}{9} - \frac{7}{18} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{7}{8} - \frac{5}{7} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

\frac{5}{6} - \frac{9}{12} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{15}{16} - \frac{3}{4} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{19}{21} - \frac{1}{7} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{5}{6} - \frac{3}{8} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{5}{9} - \frac{7}{18} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

\frac{7}{8} - \frac{5}{7} =

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

-

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

=

\frac{9}{56}

, 2.

\frac{1}{12}

, 3.

\frac{9}{12}

, 4.

\frac{20}{36}

, 5.

\frac{19}{21}

, 6.

\frac{11}{24}

, 7.

\frac{16}{21}

, 8.

\frac{20}{24}

, 9.

\frac{12}{16}

, 10.

\frac{3}{16}

, 11.

\frac{10}{12}

, 12.

\frac{3}{18}

, 13.

\frac{40}{56}

, 14.

\frac{15}{16}

, 15.

\frac{9}{24}

, 16.

\frac{14}{36}

, 17.

\frac{49}{56}

, 18.

\frac{3}{21}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

RFTyN6zJBnTSw2

Ćwiczenie 8

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

2 \frac{5}{12} - 1 \frac{1}{6} = 2

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

- 1

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

= 1

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

3 \frac{5}{13} - 1 \frac{1}{3} = 3

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

- 1

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

= 2

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

7 \frac{3}{14} - 4 \frac{1}{28} = 7

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

- 4

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

= 3

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

5 \frac{4}{5} - 3 \frac{1}{6} = 5

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

- 3

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

= 2

\frac{2}{12}

, 2.

\frac{1}{28}

, 3.

\frac{5}{30}

, 4.

\frac{19}{30}

, 5.

\frac{1}{4}

, 6.

\frac{5}{28}

, 7.

\frac{24}{30}

, 8.

\frac{13}{39}

, 9.

\frac{15}{39}

, 10.

\frac{2}{39}

, 11.

\frac{6}{28}

, 12.

\frac{5}{12}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

R1adfpDYCdzvg2

Ćwiczenie 9

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

4 \frac{1}{6} - 1 \frac{5}{12} = 4 \frac{2}{12} - 1 \frac{5}{12} = 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 2

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

3 \frac{2}{3} - 1 \frac{11}{13} = 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 2

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

7 \frac{1}{15} - 1 \frac{11}{30} = 7

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 6

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 5

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

15 \frac{1}{7} - 3 \frac{4}{8} = 15

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 14

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 11

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

Uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

4 \frac{1}{6} - 1 \frac{5}{12} = 4 \frac{2}{12} - 1 \frac{5}{12} = 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 2

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

3 \frac{2}{3} - 1 \frac{11}{13} = 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 2

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

7 \frac{1}{15} - 1 \frac{11}{30} = 7

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 6

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 1

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 5

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

15 \frac{1}{7} - 3 \frac{4}{8} = 15

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 14

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

- 3

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

= 11

\frac{9}{14}

, 2.

\frac{5}{12}

, 3.

\frac{28}{56}

, 4.

\frac{33}{39}

, 5.

\frac{3}{4}

, 6.

\frac{65}{39}

, 7.

\frac{7}{10}

, 8.

\frac{26}{39}

, 9.

\frac{14}{12}

, 10.

\frac{8}{56}

, 11.

\frac{28}{56}

, 12.

\frac{2}{30}

, 13.

\frac{32}{30}

, 14.

\frac{33}{39}

, 15.

\frac{11}{30}

, 16.

\frac{11}{30}

, 17.

\frac{32}{39}

, 18.

\frac{64}{56}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Ćwiczenie 10

Przyjrzyj się odejmowanym ułamkom i wynikom odejmowania.

\frac{1}{2} - \frac{1}{3} = \frac{1}{6}

\frac{1}{3} - \frac{1}{4} = \frac{1}{12}

\frac{1}{4} - \frac{1}{5} = \frac{1}{20}

RiQjn7GAd7Mmw

Na podstawie powyższych przykładów, uzupełnij poniższe równości odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakujące liczby dla każdej równości.

\frac{1}{5} + \frac{1}{6} =

\frac{15}{21}

, 2.

\frac{15}{56}

, 3.

\frac{14}{45}

, 4.

\frac{10}{21}

, 5.

\frac{10}{25}

, 6.

\frac{14}{30}

, 7.

\frac{11}{30}

\frac{1}{3} + \frac{1}{7} =

\frac{15}{21}

, 2.

\frac{15}{56}

, 3.

\frac{14}{45}

, 4.

\frac{10}{21}

, 5.

\frac{10}{25}

, 6.

\frac{14}{30}

, 7.

\frac{11}{30}

\frac{1}{9} + \frac{1}{5} =

\frac{15}{21}

, 2.

\frac{15}{56}

, 3.

\frac{14}{45}

, 4.

\frac{10}{21}

, 5.

\frac{10}{25}

, 6.

\frac{14}{30}

, 7.

\frac{11}{30}

\frac{1}{7} + \frac{1}{8} =

\frac{15}{21}

, 2.

\frac{15}{56}

, 3.

\frac{14}{45}

, 4.

\frac{10}{21}

, 5.

\frac{10}{25}

, 6.

\frac{14}{30}

, 7.

\frac{11}{30}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Dodawanie i odejmowanie ułamków

R14PJEdLCTKjv31

Ćwiczenie 11

Benedykt ma w swojej biblioteczce książki przygodowe i książki o rowerach. Książki przygodowe stanowią

\frac{14}{17}

jego księgozbioru. Jaką część księgozbioru Benedykta stanowią książki o rowerach? Uzupełnij poniższą lukę. Kliknij w nią, aby rozwinąć listę, a następnie wybierz poprawną odpowiedź. Odpowiedź: Książki o rowerach stanowią 1.

\frac{4}{17}

, 2.

\frac{5}{17}

, 3.

\frac{3}{17}

, 4.

\frac{2}{17}

księgozbioru.

Benedykt ma w swojej biblioteczce książki przygodowe i książki o rowerach. Książki przygodowe stanowią $\frac{14}{17}$ jego księgozbioru. Jaką część księgozbioru Benedykta stanowią książki o rowerach?

$\frac{5}{17}$ , $\frac{2}{17}$ , $\frac{4}{17}$ , $\frac{3}{17}$

Poprawna odpowiedź to: ............ księgozbioru.

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

R1QmRGdbut7a231

Ćwiczenie 12

Przez

\frac{1}{9}

lekcji pani od matematyki zazwyczaj wita się z uczniami i sprawdza obecność. Tyle samo zajmuje jej sprawdzenie pracy domowej, a przez

\frac{1}{12}

lekcji pani zadaje nową pracę domową. Jaką część lekcji trwają pozostałe jej etapy? Uzupełnij poniższą lukę. Kliknij w nią, aby rozwinąć listę, a następnie wybierz poprawną odpowiedź. Odpowiedź: Pozostałe etapy lekcji stanowią 1.

\frac{23}{36}

, 2.

\frac{27}{36}

, 3.

\frac{29}{36}

, 4.

\frac{25}{36}

lekcji.

Przez $\frac{1}{9}$ lekcji pani od matematyki zazwyczaj wita się z uczniami i sprawdza obecność. Tyle samo zajmuje jej sprawdzenie pracy domowej, a przez $\frac{1}{12}$ lekcji pani zadaje nową pracę domową. Jaką część lekcji trwają pozostałe jej etapy?

$\frac{29}{36}$ , $\frac{23}{36}$ , $\frac{25}{36}$ , $\frac{27}{36}$

Poprawna odpowiedź to: ............ lekcji.

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

R8X4gqacbKCjv31

Ćwiczenie 13

Na przedstawieniu dla dorosłych trzy piąte widowni zajęły kobiety, a jedną trzecią – mężczyźni. Jaka część widowni nie została zajęta przez widzów?

$\frac{4}{15}$ , $\frac{2}{15}$ , $\frac{3}{15}$ , $\frac{1}{15}$

Poprawna odpowiedź to: ............ widowni.

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

R1Zwp1Cp6VQmN3

Ćwiczenie 14

Oblicz, pamiętając o kolejności wykonywania działań, a następnie uzupełnij luki odpowiednimi liczbami. Kliknij w lukę, aby rozwinąć listę i wybierz brakującą liczbę dla każdej równości.

\frac{1}{3} + \frac{2}{5} - \frac{3}{15} =

\frac{11}{12}

, 2.

\frac{8}{15}

, 3.

4 \frac{5}{8}

, 4.

\frac{15}{21}

, 5.

\frac{13}{21}

, 6.

1 \frac{29}{60}

, 7.

4 \frac{7}{8}

, 8.

3 \frac{4}{9}

, 9.

1 \frac{37}{50}

\frac{1}{7} + \frac{2}{3} - \frac{4}{21} =

\frac{11}{12}

, 2.

\frac{8}{15}

, 3.

4 \frac{5}{8}

, 4.

\frac{15}{21}

, 5.

\frac{13}{21}

, 6.

1 \frac{29}{60}

, 7.

4 \frac{7}{8}

, 8.

3 \frac{4}{9}

, 9.

1 \frac{37}{50}

1 \frac{1}{2} - \frac{5}{6} + \frac{3}{12} =

\frac{11}{12}

, 2.

\frac{8}{15}

, 3.

4 \frac{5}{8}

, 4.

\frac{15}{21}

, 5.

\frac{13}{21}

, 6.

1 \frac{29}{60}

, 7.

4 \frac{7}{8}

, 8.

3 \frac{4}{9}

, 9.

1 \frac{37}{50}

\frac{1}{3} + (1 \frac{3}{4} - \frac{3}{5}) =

\frac{11}{12}

, 2.

\frac{8}{15}

, 3.

4 \frac{5}{8}

, 4.

\frac{15}{21}

, 5.

\frac{13}{21}

, 6.

1 \frac{29}{60}

, 7.

4 \frac{7}{8}

, 8.

3 \frac{4}{9}

, 9.

1 \frac{37}{50}

4 \frac{1}{3} + (\frac{3}{4} - \frac{3}{8} - \frac{1}{12}) =

\frac{11}{12}

, 2.

\frac{8}{15}

, 3.

4 \frac{5}{8}

, 4.

\frac{15}{21}

, 5.

\frac{13}{21}

, 6.

1 \frac{29}{60}

, 7.

4 \frac{7}{8}

, 8.

3 \frac{4}{9}

, 9.

1 \frac{37}{50}

2 \frac{1}{3} + (2 \frac{1}{18} - \frac{5}{6} - \frac{1}{9}) =

\frac{11}{12}

, 2.

\frac{8}{15}

, 3.

4 \frac{5}{8}

, 4.

\frac{15}{21}

, 5.

\frac{13}{21}

, 6.

1 \frac{29}{60}

, 7.

4 \frac{7}{8}

, 8.

3 \frac{4}{9}

, 9.

1 \frac{37}{50}

Źródło: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.