# 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 $\underline{£1.05}$.*