Dzielenie ułamków zwykłych

Learning objectives

You will discover the methods of division the common fractions.

Learning effect

• You convert the natural number by the common fraction.

• You divide the fraction by the fraction.

• You specify the reciprocal of given number.

• You solve the task using the division of the fractions.

• You use English to describe the method of dividing common fractions.

Today you are going to discover the method of dividing the common fractions.

Prepare two sets of cards with numbers from $1$ to $9$. Draw two cards of the first set and make the common fractioncommon fractioncommon fraction of it. The letter of the first card is the numerator, the letter of the other card is the denominator of the fraction. Use the pencil as a fraction bar. Then, use the other set of the cards to make such a fraction that the product of both fractions equals $1$.

Conclusion:

If the product of two fractions different from zero equals $1$ , they are reciprocal of one another.

Conclusion:

• The number 0 has not the reciprocal.

• The reciprocal of number $1$ is $1$.

Analyse the example below.

The cake was divided into identical parts, each of them was $\frac{1}{6}$ part of the cake. How many pieces was the cake divided into?

$1:\frac{1}{6}=6$

Answerm6901f5edee07edc1_1533277756654_0Answer

Watch the slideshow. You are going to learn the method of division the natural numbernatural numbernatural number by the mixed numbermixed numbermixed number.

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Pokaz slajdów przedstawia w jaki sposób dzielimy liczbę naturalną przez liczbę mieszaną. Instrukcja obsługi z poziomu klawiatury: 1. Uruchomienie aplikacji - ENTER, 2. Na każdym ze slajdów czytany jest automatycznie tekst alternatywny po polsku, 3. Przy pierwszym uruchomieniu na pierwszym slajdzie, czytanie tekstu po angielsku - TAB, 4. Przejście między slajdami: do następnego slajdu - TAB, do poprzedniego slajdu - TAB + SHIFT, 5. Przejście do czytania napisu po angielsku - strzałka w górę + strzałka w dół (czyta tekst po angielsku widoczny na slajdzie).

Pokaz slajdów przedstawia w jaki sposób dzielimy liczbę naturalną przez liczbę mieszaną. Instrukcja obsługi z poziomu klawiatury: 1. Uruchomienie aplikacji - ENTER, 2. Na każdym ze slajdów czytany jest automatycznie tekst alternatywny po polsku, 3. Przy pierwszym uruchomieniu na pierwszym slajdzie, czytanie tekstu po angielsku - TAB, 4. Przejście między slajdami: do następnego slajdu - TAB, do poprzedniego slajdu - TAB + SHIFT, 5. Przejście do czytania napisu po angielsku - strzałka w górę + strzałka w dół (czyta tekst po angielsku widoczny na slajdzie).

Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/Dm02uYzhE

Conclusion:

To divide the natural numbernatural numbernatural number by the fraction, the number should be multiplied by the reciprocal of the fraction.

The students divide the natural numbers by the mixed numbers.

Conclusion:

To divide the natural numbernatural numbernatural number by the mixed numbermixed numbermixed number we should convert the mixed numbermixed numbermixed number to the improper fraction first, then divide the natural number by the fraction.

Look at the example below:

$\frac{3}{4}:\frac{5}{7}=\frac{3}{4}·\frac{7}{5}=\frac{3·7}{4·5}=\frac{21}{20}=1\frac{1}{20}$

Conclusion:

To divide the common fractioncommon fractioncommon fraction by the other common fractioncommon fractioncommon fraction we should multiply the first fraction by the reciprocal of the second one.

Conclusion:

When the dividend or the divisor is a mixed numbermixed numbermixed number it should be converted to the improper fraction.

Remember:

1. If the product of two fractions different from zero equals $1$, they are reciprocal of one another. To divide the natural numbernatural numbernatural number by the fraction , the number should be multiplied by the reciprocal of the fraction.

2. To divide the natural numbernatural numbernatural number by the mixed numbermixed numbermixed number we should convert the mixed numbermixed numbermixed number to the improper fraction first, then divide the natural numbernatural numbernatural number by the fraction.

3. To divide the common fractioncommon fractioncommon fraction by the other common fractioncommon fractioncommon fraction we should multiply the first fraction by the reciprocal of the second one.

4. When dividend or divisor is a mixed numbermixed numbermixed number it should be converted to the improper fraction.

Check what you have learned by doing the following tasks.

Exercises

Glossary

Keywords

common fractioncommon fractioncommon fraction

mixed numbermixed numbermixed number

natural numbernatural numbernatural number

quotientquotientquotient

reciprocal of the numberreciprocal of the numberreciprocal of the number