Operation with common fractions

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Działania na ułamkach zwykłych

Learning objectives

Developing the ability of doing the operations with the common fractions.

Learning effect

You do the operations with the common fractions.
You solve the text task using the operations with the fractions.
You use English to describe the order of operations with the fractions.

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Source: GroMar, licencja: CC BY 3.0.

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nagranie abstraktu

Today you are going to develop the ability of doing the operations with the fractions. Prepare the cards with the following fractions: $1 \frac{3}{4}$ , $2 \frac{1}{2}$ , $3 \frac{4}{5}$ , $7 \frac{5}{6}$ , $\frac{4}{7}$ , $2 \frac{3}{8}$ , $1 \frac{2}{9}$ , $5 \frac{9}{10}$ and bring them to the class. Put the cards on the desk. Draw two fractions, choose the operation which you are going to complete (addition, subtraction, multiplication, division). Write the appropriate calculations in your notebook. Repeat the activity for few times.

Task 1

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nagranie abstraktu

Watch the slideshow. You are going to watch the order of the operations with the fractions.

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Source: GroMar, licencja: CC BY 3.0.

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nagranie abstraktu

Conclusion:

The order of the operations with the fractions:

Firstly we do the operations in brackets.
Then exponentiation, multiplication or division (in order they appear).
Finally the addition or subtraction (in order they appear).

Task 2

Calculate:

a) $\frac{2}{15} + \frac{4}{5} \cdot \frac{1}{3}$

b) $(\frac{2}{5} + \frac{3}{4}) \div 6 \frac{2}{3}$

c) $3 \frac{1}{5} \cdot (5 \frac{1}{4} - 1 \frac{3}{4})$

d) $1 \frac{3}{7} - \frac{3}{7} \cdot \frac{2}{3}$

Task 3

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nagranie abstraktu

In a bottle there is $\frac{1}{3}$ of a litre of juice, in a jug $\frac{1}{2}$ of a litre more. How much more of the juice is in the jug than in the bottle?

Task 4

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nagranie abstraktu

Calculate:

a) $(\frac{2}{3})^{3}$

b) $(1 \frac{2}{5})^{2}$

Task 5

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nagranie abstraktu

Michael picked up $\frac{2}{9}$ of a litre of wild strawberries, John $\frac{4}{9}$ of a litre, and Tom $\frac{5}{9}$ of a litre. Did these three friends pick up more or less wild strawberries than one litre?

Task 6

An extra task:

In a class $\frac{1}{3}$ of all the students go to the swimming lesson, and four students more what means half a class attend the dancing classes. How many students are there in that class?

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nagranie abstraktu

Remember:

When we do the operations with the common fractions we:
Firstly we do the operations in brackets.
hen exponentiation, multiplication or division (in order they appear).
Finally the addition or subtraction (in order they appear).
Check what you have learned by doing the following tasks.

Exercises

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Exercise 1

Determine which sentences are true.

$1 \frac{5}{12} \div 1 \frac{7}{10} = \frac{5}{6}$
$1 \frac{2}{8} \cdot 3 \frac{1}{5} = 2 \frac{1}{4}$
$7 \frac{1}{3} - 2 \frac{1}{2} = 4 \frac{5}{6}$
$9 \frac{2}{3} + 5 \frac{9}{11} = 16 \frac{17}{33}$

zadanie

Source: GroMar, licencja: CC BY 3.0.

Exercise 2

The Christmas decoration was made of 400 multi‑coloured stars – bigger and smaller ones. The big stars were $\frac{2}{5}$ of all stars and $\frac{3}{8}$ of the small stars was gold. How many small golden stars were used for the Christmas decoration?

Exercise 3

Mr Kowalski sawed the $\frac{4}{9}$ of the field with the rye, $\frac{1}{5}$ of the field with the oats. The half of the remaining rest of the field he leased to his best friend Mr Nowak. What part of the field does Mr Nowak rent?

Describe the order of the operations with fractions in English.

$\frac{8}{45}$ of the field.

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Exercise 4

Indicate which pairs of expressions or words are translated correctly.

dodawanie ułamków - addition of the fractions
odejmowanie ułamków - subtraction of the fractions
mnożenie ułamków - multiplication of the fractions
dzielenie ułamków - division of the fractions
odwrotność liczby - mixed number
ułamek nieskracalny - reducible fraction

zadanie

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Match Polish terms with their English equivalents.

mnożenie ułamków
multiplication of the fractions
addition of the fractions
division of the fractions
odwrotność liczby
dodawanie ułamków
subtraction of the fractions
odejmowanie ułamków
reciprocal of the number
dzielenie ułamków

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

Glossary

addition of the fractions

dodawanie ułamków

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wymowa w języku angielskim: addition of the fractions

subtraction of the fractions

odejmowanie ułamków

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wymowa w języku angielskim: subtraction of the fractions

multiplication of the fractions

mnożenie ułamków

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wymowa w języku angielskim: multiplication of the fractions

division of the fractions

dzielenie ułamków

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wymowa w języku angielskim: division of the fractions

reciprocal of the number

odwrotność liczby

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wymowa w języku angielskim: reciprocal of the number

reducible fraction

ułamek skracalny

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wymowa w języku angielskim: reducible fraction

irreducible fraction

ułamek nieskracalny

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wymowa w języku angielskim: irreducible fraction

mixed number

liczba mieszana

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wymowa w języku angielskim: infrasound

order of operations

kolejność wykonywania działań

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wymowa w języku angielskim: the order of operations

improper fraction

ułamek niewłaściwy

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wymowa w języku angielskim: improper fraction

Keywords

addition of the fractionsaddition of the fractionsaddition of the fractions

subtraction of the fractionssubtraction of the fractionssubtraction of the fractions

multiplication of the fractionsmultiplication of the fractionsmultiplication of the fractions

division of the fractionsdivision of the fractionsdivision of the fractions

reciprocal of the numberreciprocal of the numberreciprocal of the number

Scenariusz

Exercises

Glossary

Keywords