How_To_Be_Good_At_Math

100

Scaling and

fractions

As we’ve just seen,

we can also scale with

fractions. Multiplying

withproper fractions,

which are fractions

less than one, makes

numbers smaller,

not bigger.

Multiplication

as scaling

The second building is twice

as tall as the first, so its

height has been scaled up by a

factor of 2. We can write this as:

10 × 2 = 20

Look at these three buildings.

They are all different heights.

The third building is two

times taller than the

second, so we can say it’s been

scaled up by a factor of 2. We

can write this as: 20 × 2 = 40

The third building is

four times taller than

the first. It has been

scaled up by a factor of

4. We can write this as:
   10 × 4 = 40

We could also see

each building as

being scaled down. The

second building is half

the height of the third

building. We can write

this using a fraction:

40 ×^1 ⁄ 2 = 20

Look at this calculation. We want to

multiply^1 ⁄ 4 by^1 ⁄ 2.

Look at this shape. It’s a quarter of a

circle. To multiply a quarter by a half, we

simply need to take away half of the quarter.

You can see that half of the quarter is

one-eighth of a circle.

So,^1 ⁄ 4 ×^1 ⁄ 2 =^1 ⁄ 8

Repeated addition is not the only way to think about

multiplication. When we change the size of an object,

we carry out a kind of multiplication called scaling.

We also use scaling when we multiply with fractions.

We use scaling to

change the sizes of

objects and to multiply

with fractions.

CALCULATING • MULTIPLICATION AS SCALING

(^1) ⁄ 4 of a circle
× =?
× =
Half of^1 ⁄ 4
of a circle
1
2
1
2
1
4
1
4
1
8
40 m
20 m
10 m
1
8
1
8
1
4
100_101_Multiplication_as_scaling_Factor_pairs.indd 100 29/02/2016 14:48