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?

$$£4\div£2=2$$

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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 $$\underline{£1.05}$$.