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7.3 Multiplying fractions

7.3 Multiplying fractions

You already know how to multiply an integer by a fraction and multiply a fraction by a fraction.
You can complete multiplications more easily by cancelling common factors before you multiply.

Worked example 7.3
15
Work out: a 2 × 18 b 3 × 26 c 5 × 4 d 2 × 14 e 4 × 22
5
3
4
7
15
7
9
6
a 2 × 18 Divide 3 and 18 by 3. The 3 cancels to 1 and the 18 cancels to 6.
1 3
= 2 × 6 = 12 2 is the same as 2, so just work out 2 × 6. 2 × 6 = 12.
1
3
b × 26 13 4 won’t divide into 26, but 4 and 26 can both be divided by 2 to give 2 and 13.
2 4 3 39 39
= 2 ×13 = 2 3 × 13 = 39, so the answer is 2 .
1
= 19 This is an improper fraction, so change it to a mixed number.
2
5 4 5 × 4
c 7 × 9 = 7 × 9 There are no common factors between the numbers in the numerators and
denominators, so simply multiply 5 by 4 and 7 by 9.
= 20 20 cannot be cancelled further and is a proper fraction.
63 2 63
d 2 7 × 14 7 divides into 7 and 14 to give 1 and 2. There are no other common factors.
15
1
2
2
2 × 15 = 2 × 15 Now multiply 2 by 2 and 1 by 15.
1 ×
1
4 4
= 15 = 15 cannot be cancelled further and is a proper fraction.
2 4 15 3
×
e 5 22 5 divides into 5 and 15 to give 1 and 3, 4 and 22 can be divided by 2
1 11 to give 2 and 11.
×
3
2 × 11 = 23 Now multiply 2 by 3 and 1 by 11.
111×
1
6
6
= 11 = 11 cannot be cancelled further and is a proper fraction.
) Exercise 7.3
1 Work out these multiplications. Cancel common factors before multiplying.
a 3 × 12 b 5 × 28 c 4 × 45 d 3 × 72 e 7 × 132 f 7 × 180
4 7 5 8 11 9
2 Work out these multiplications. Cancel common factors before mutliplying.
Write each answer as a mixed number in its simplest form.
a 3 × 36 b 4 × 39 c 5 × 8 d 7 × 45 e 1 × 30 f 9 × 35
8 9 6 10 12 14
3 Work out these multiplications. Cancel common factors before multiplying when possible.
Write each answer in its lowest terms.
5
5
2
5
3
a 3 × b 4 × c 9 × d 6 × e 3 × f 8 × 3
4 7 5 8 11 5 7 9 8 6 9 13
8
g 4 × 5 h 3 × i 2 × 15 j 5 × 6 k 4 × 15 l 8 × 9
5 12 4 9 5 16 9 25 9 22 21 20
68 7 Fractions