Two quantities are in direct proportion when they increase or decrease in the same ratio. For example, you could increase something by doubling it, or decrease it by halving.

Here is a typical problem:


Twelve pencils cost {72}{p}. Find the cost of {30} pencils.

To solve this problem, we need to know the cost of one pencil.

We know that {12} pencils cost {72}{p}, so if we divide {72} by {12} to give us the cost of one pencil:

72 \div 12 = 6

So {1} pencil costs {6}{p}. Now we need to know the cost of 30 pencils. We multiply {6}{p} by {30}.

6 \times 30 = 180p

So {30} pencils cost \pounds 1.80.

If you had a problem working out the answer, the basic method to remember is to divide by how many you know, then multiply by what you want to know.

Now try this one:


Jenny buys {15} felt-tip pens. It costs her \pounds 2.85. How much would {20} pens have cost?

The answer is \pounds 3.80.

You divide \pounds 2.85 by {15}, then multiply the answer by {20}.

  • {15} pens cost \pounds 2.85
  • {1} pen costs \pounds2.85\div15=\pounds0.19 (or {19} pence)
  • So {20} pens would cost \pounds0.19\times20=\pounds3.80
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