Unit 20 Section 3 : Multiplying Fractions

To multiply two fractions, we multiply the two numerators (top numbers) together to get the new numerator, and we multiply the two denominators (bottom numbers) together to get the new denominator.

a	×	c	=	a × c
b		d		b × d

Sometimes some cancelling-down can happen before the numerators and denominators are multiplied together.

If there are whole numbers or mixed numbers, these can be converted into top-heavy fractions and multiplied in the same way.

Example 1

Work out:	4	×	3
	7		5

The answer is	4 × 3	=	12
	7 × 5		35

 
Example 2 (with cancelling down before multiplying)

Work out:	3	×	4
	10		9

At this stage we can cancel numerators with denominators if they are both divisible by the same number.
For example, 4 and 10 are both divisible by 2, so we can divide them both by 2 and the answer will be the same.

	3	×	4 2
	10 5		9

In a similar way 3 and 9 can be cancelled as they are both divisible by 3.

	3 1	×	4 2
	10 5		9 3

Now the fractions can be multiplied:

The answer is	1 × 2	=	2
	5 × 3		15

NOTE: You can only cancel a numerator with a denominator, not two numerators or two denominators.

 
Example 3 (with a whole number in the question)

NOTE: If a whole number appears in a question, it can be converted to a top-heavy fraction because N =	N
	1

Work out:	15	×	3
			5
This becomes:	15	×	3
	1		5

Now the multiplication can be pre-cancelled:

	15 3	×	3
	1		5 1

Finally we can do the multiplication:

The answer is	3 × 3	=	9	= 9
	1 × 1		1

NOTE: Some people prefer to answer this type of question by dividing 15 by 5 to get one fifth of 15 (which is 3)
and then multiply the answer by 3 to get three fifths of 15 (which is 9). This is also a valid method and can be used.

 
Example 4 (with mixed numbers in the question)

If there is a mixed number in the question, it must be converted into a top-heavy fraction before multiplying.

Work out:	1	3	×	2	2
		4			3
This becomes:	7		×	8
	4			3

We can now pre-cancel and carry out the multiplication as normal:

7	×	8	=	7	×	8 2	=	14
4		3		4 1		3		3

NOTE: We could write this as a mixed number 4	2	but often we will just leave the answer as a top-heavy fraction.
	3

Practice Question

(a)	5	×	2
	7		3

(b)	4	×	5
	5		12

(c)	3	×	12
	4

(d)	1	1	×	2	2
		2			7

Exercises

Question 1
Calculate the answer to each multiplication, and remember to make sure your answer is in its simplest form.

(a)	1 × 1        2 3
(b)	1 × 1 2 2
(c)	1 × 1 3 4
(d)	2 × 3 3 4
(e)	3 × 4 7 5
(f)	3 × 3 8 4
(g)	4 × 2 7 9
(h)	6 × 3 7 8
(i)	5 × 5 6 7
(j)	3 × 3 10 7
(k)	1 × 3 2 19
(l)	4 × 2 11 3

Question 2
Calculate the answer to each multiplication. All the answers in this question are whole numbers.

(a)	1 × 15        5
(b)	1 × 32 8
(c)	7 × 16 8
(d)	3 × 14 7
(e)	3 × 28 4
(f)	4 × 30 5
(g)	21 × 5        7
(h)	24 × 5 8
(i)	18 × 5 9
(j)	66 × 2 3
(k)	34 × 4 17
(l)	57 × 5 19

Question 3
Calculate the answer to each multiplication, and leave your answer as a top-heavy fraction in its simplest form.

(a)	1 1 × 3        2 4
(b)	5 1 × 2 2 3
(c)	1 3 × 2 4 5
(d)	1 3 × 1 7 2
(e)	4 1 × 1 4 5
(f)	3 1 × 1 7 3
(g)	1 1 × 1 4        2 5
(h)	1 1 × 1 1 2 2
(i)	1 2 × 1 1 3 2
(j)	1 1 × 2 1 4 2
(k)	3 1 × 2 1 4 3
(l)	1 1 × 2 1 4 5

Question 4
Calculate the area of each of the rectangles below. Simplify your answer and write it as a mixed number.

(a)		m²
(b)		m²
(c)		m²
(d)		m²

Question 5 James is making a cake. The recipe he is using says that he needs	3	kg of flour.
	4

Work out how much flour is needed to make:

(a) 2 cakes	kg
(b) 6 cakes	kg
(c) 10 cakes	kg

Question 6 Jan goes shopping and buys	3	kg of cheese. She keeps	2	of it and gives the other	1	of it to her sister.
	4		3		3

Work out the weight of:

(a) the cheese Jan keeps	kg
(b) the cheese Jan gives to her sister?	kg