How_To_Be_Good_At_Math

54 NUMBERS •^ MULTIPLYING FRACTIONS

Multiplying by

whole numbers

and by fractions

What happens when we

multiply by a fraction?

Let’s multiply 4 by a

whole number, and

by a proper fraction.

Remember, a proper

fraction is less than 1.

Multiplying fractions

Let’s look at how to multiply a fraction by a whole number

or by another fraction.

Multiplying by a fraction

Multiplying 4 by^1 / 2 makes 2.

When we multiply by a proper

fraction, the answer is always

smaller than the original number.

Multiplying by a whole number

When we multiply 4 by 2, we get 8.

This is what we’d expect – that

multiplying a number makes it bigger.

Multiplying a fraction by a whole number

Let’s look at some different calculations to work out what happens when we multiply fractions.

4 × 2 = 8

1

2

Let’s try the calculation

(^1) / 2 × 3. This is the same as
three groups of one half, so we
can add three halves together on
a number line to make 1^1 / 2.
Now let’s work out^3 / 4 × 3 on
a number line. If we add all
the quarters in three groups of
three-quarters, we get 2^1 /4.
To work out the same
calculations without a
number line, we simply multiply
the whole number by the
fraction’s numerator, like this.
(^01) ⁄ 2 1
(^1) ⁄ 2 1 1 ⁄ 2
(^1) ⁄ 2 21 2 1 ⁄ 2
(^01) 2 2^1 ⁄ 4
3
3
= 2
(^1) or
2
1 × 3
× 2 = 2
Three groups of one
half make 1^1 ⁄ 2
The answer is smaller than
the original number
The answer is larger than
the original number
Three groups of
three-quarters
make 2 1 / 4
3
9
= 4
34 3 × 3 or
× 4 = 2
1
4
4 × = 2
3
4
3
4
3
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1
4
1
2
1
2
1
2
1
2
054-055_Multiplying_Fractions.indd 54 29/02/2016 14:09