April 10, 2023

Multiplication and division of fractions

1. Multiplying fractions

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April 10, 2023

8

3838

8

A simple fractionNumerator

Denominator

You can think of any fraction as the number 1 multiplied by the numerator, then divided by the denominator.

1 3 ÷×

This is the same as 11

3× 11

38

××

or

What happens when you multiply by a fraction?

You can think of this as the number 2 multiplied by the numerator, then divided by the denominator.

÷

2 ×

Explanation

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April 10, 2023

21

38

××

2 ×What happens when you multiply by a fraction? 38

You can think of this as the number 2 multiplied by the numerator, then divided by the denominator.

8

82 3 ÷×

This is the same as 21

3× or

÷

=68

34=

Explanation

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April 10, 2023ExplanationWhen you multiply two fractions together, you can think of it as working out what amount the first fraction of the second fraction would be.

12

of = =18

or

=×12

14

18

Notice that all you have to do is first multiply the two numerators and then multiply the two denominators.

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April 10, 2023

=

35

12

×3

10=

34

13

×3

12= =

14

351

343×

85 4

15× =

12020 6=

Examples

In the next example, you can simplify your answer…

Remember, when you have mixed fractions, you must multiply the whole number by the denominator, then add your answer to the numerator…

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April 10, 2023

34

16

×3

24= =

Simplifying by cancelling

These two fractions have been multiplied together, then the answer simplified.

If a numerator in one fraction has a common factor with the denominator in the other fraction, you can cancel down the fractions, before carrying out the multiplication.

Cross out the numbers with the common factor 3 and replace them with the quotients for that factor .

1

2

18

Explanation

18

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