R1SI3r42jhkfA

Operations on common and decimal fractions

Source: licencja: CC 0.

Działania na ułamkach zwykłych i dziesiętnych

Learning objectives

  • You will learn to do operations on common and decimal fractions and apply this skill to do text exercises.

Learning effect

  • You do operations on common and decimal fractions and apply this skill to do text exercises.

R1K20q1neRMCo1
nagranie abstraktu

Revise rules of operations on common fractions and rules of operations on decimal fractions.

Task 1
R9vTyCdedxf5G1
nagranie abstraktu

Open the interactive illustration and think about what operation needs to be done first to be able to add common and decimal fractiondecimal fractiondecimal fraction.

Rn7wEmtRFBRzN
Ilustracja interaktywna przedstawia dwie części pizzy. Część oznaczona numerami jeden i dwa stanowi połowę, część oznaczona numerami trzy i cztery stanowi czwartą część tej pizzy. Po prawej stronie kartka w kratkę z napisem ułamek zwykły jedna czwarta dodać ułamek dziesiętny pięć dziesiątych równa się znak zapytania. Na ilustracji widoczne są numery, a na nich podpisy. 1. A half of pizza is 0,5 of pizza {audio}, 2. A half of pizza is ½ of pizza {audio}, 3. A fourth of pizza is 0,25 of pizza {audio}, 4. A fourth of pizza is ¼ of pizza {audio}.
Operations on common and decimal fractions
Source: GroMar, licencja: CC BY 3.0.

After having completed the exercise, they draw a conclusion and compare it with the following one.

Conclusion:

R1S0XzvX17Zhd1
nagranie abstraktu
  • If there are both common and decimal fractions in calculations, we need to convert them to the same form, that is convert common fractions to decimals or decimals to common fractions and then do calculations.

RtOzuWt1HDq6O1
nagranie abstraktu

Think if we can always convert a common fractioncommon fractioncommon fraction into a decimal and a decimal into a common fractions. Revise methods of converting fractionsconverting fractionsconverting fractions. Do you have following information in your notes?

  • decimal fractiondecimal fractiondecimal fraction can always be converted into a common fractioncommon fractioncommon fraction by writing it using the fraction bar.

  • A common, simplified fraction can be converted into a decimal only if the only divisorsdivisorsdivisors of its denominator are numbers 2 or 5.

Using obtained knowledge, do three exercises from each region.

Task 2

Region I – addition.

R27P9nSgusSc41
nagranie abstraktu

Tasks for 1 point.

1. Do the addition: 12+0,75

2. Do the addition: 1,25+16

3. Do the addition: 429+3,7

4. Do the addition: 5310+6,5

Task for 2 points.

5. Mum made a drink out of 4,75 kg of plums, 318 kg of apples 212 kg of strawberries. How many kilograms of fruits did she use?

Task 3

Region II – subtraction.

R3w81PzKEmzyF1
nagranie abstraktu

Tasks for 1 point.

1. Do the subtraction: 560,125

2. Do the subtraction: 2270,6

3. Do the subtraction: 12,05318

4. Do the subtraction: 18150,25

Task for 2 points.

5. Ania bought green ribbon and 434 m of blue ribbon. How many metres of green ribbon did she buy if together there was 8,5 m of ribbon?

Task 4

Region III – multiplication.

R1ZfRyjctWVV11
nagranie abstraktu

Tasks for 1 point.

1. Do the multiplication: 470,28

2. Do the multiplication: 5351,5

3. Do the multiplication: 0,21227

4. Do the multiplication: 92,03110000

Task for 2 points.

5. A kilogram of pears costs 3,3 zł. How much will we pay for 13 kg of pears?

Task 5

Region IV – division.

RWgBXTnMSLE5M1
nagranie abstraktu

Tasks for 1 point.

1. Do the division: 625:0,6

2. Do the division: 0,48:117

3. Do the division: 5,5:234

4. Do the division: 214:0,75

Task for 2 points.

5. The area of a rectangle is 6,25 cmIndeks górny 2, and the length of one side is 212 cm. Calculate the length of the other side of the rectangle.

Task 6

An extra task:

The quotientquotientquotient of two numbers is equal to 416, and the divisor is 22930 smaller than the quotient. Calculate the dividend.

Remember:

RI5Fjx1VC2QTr1
nagranie abstraktu
  • If there are both common and decimal fractions in calculations, we need to convert them to the same form, that is convert common fractions to decimals or decimals to common fractions and then do calculations.

  • decimal fractiondecimal fractiondecimal fraction can always be converted into a common fractioncommon fractioncommon fraction by writing it using the fraction bar.

  • A common, simplified fraction can be converted into a decimal only if the only divisorsdivisorsdivisors of its denominator are numbers 2 or 5.

Do the revision exercises.

Exercises

Exercise 1
R3RPmYdbWU2mv
Wersja alternatywna ćwiczenia: The number 13 is the result of the division. Możliwe odpowiedzi: 1. 3,5-223, 2. 214+0,75, 3. 812:0,25, 4. 123·0,2
zadanie
Source: GroMar, licencja: CC BY 3.0.
Exercise 2

Calculate by how much the sum of numbers 538 and 0,25 is greater than the product of these numbers.

Exercise 3

Kasia bought a kilogram of apples and a kilogram of peaches and she paid 12,5 zł. Calculate the price of 1 kg of these fruits if we know that the price of 1 kilogram of apples is 14 of the price of 1 kilogram of peaches. Give the solution and the answer in English.

Exercise 4
R3Tnmdw4Sot7k
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. ułamek dziesiętny - decimal fraction, 2. ułamek zwykły - common fraction, 3. zamiana ułamków - converting fractions, 4. działania na ułamkach - operation on fractions, 5. wynik działania - difference, 6. iloczyn - quotient
zadanie
Source: GroMar, licencja: CC BY 3.0.
RGRy2Yf0q28vj1
Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

converting fractions
converting fractions

zamiana ułamków

RIHUjZs1KYdpf1
wymowa w języku angielskim: converting fractions
common fraction
common fraction

ułamek zwykły

RAdh2jMGMpJzl1
wymowa w języku angielskim: common fraction
decimal fraction
decimal fraction

ułamek dziesiętny

RjhaIGLTT6lrE1
wymowa w języku angielskim: decimal fraction
difference
difference

różnica

Rc2aCwQNyzWcp1
wymowa w języku angielskim: difference
divisors
divisors

dzielniki

R1dr4FVrbRdoX1
wymowa w języku angielskim: divisors
operation on fractions
operation on fractions

działania na ułamkach

Rkor9DkAKLjk91
wymowa w języku angielskim: operation on fractions
product
product

iloczyn

R1LGPNV0IbgNj1
wymowa w języku angielskim: product
quotient
quotient

iloraz

RaOUwEjXlN3jc1
wymowa w języku angielskim: quotient
result of the operation
result of the operation

wynik działania

RAVzqxku5Tux51
wymowa w języku angielskim: result of the operation
sum
sum

suma

Rw8c3tkAEzgNG1
wymowa w języku angielskim: sum

Keywords

common fractioncommon fractioncommon fraction

decimal fractiondecimal fractiondecimal fraction

operation on fractionsoperation on fractionsoperation on fractions

result of the operationresult of the operationresult of the operation