Multiplication scaling problems

In a nutshell

Multiplication scaling, or integer scaling, is a method of comparing different values. You are given some information and have to apply it to smaller or larger values in order to solve a problem.

Identifying integer scale

By identifying the multiplication scale being used, you can apply scaling to help find new amounts.

Example 1

Adam bought $3$ apples for $£2$ . Sally bought $£4$ worth of apples. What scale has been used in this example? How many apples did Sally buy?

$£4\div£2=2$

Sally has spent $2$ times more than Adam.

The scale is $\underline{2}$ .

$3$  apples $\times 2 = 6$ apples

Sally bought $\underline{6}$ apples.

Note: When identifying a scale, divide two values which have the same units. In the scenario above this was pounds ( $£$ ).

Applying integer scaling

Integer scaling can be used to calculate a new value by multiplying an old value by the scale.

Example 2

Jerome buys $4$  cakes for $£5$ . Ahmed wants to buy $3$ times more cakes. How much will this cost him?

$3\times 5 = 15$

Ahmed will pay $\underline{£15}$ .

Example 3

$2$ crayons cost $35p$ . How much will $6$ crayons cost?

Find the scale by dividing the new amount of crayons $(6)$ by the old amount of crayons $(2)$ .

$6\div2=3$

Multiply the cost of $2$ crayons, $35p$ , by the scale.

$35p \times 3 = 105p = £1.05$ 

Therefore, $6$ crayons will cost $\underline{£1.05}$ .