Ratios are usually written in the form a:b and can be used on maps to show the scale in relation to real life. Two quantities are in direct proportion when they increase or decrease in the same ratio.

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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:

- Question
Twelve pencils cost . Find the cost of pencils.

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

We know that pencils cost , so if we divide by to give us the cost of one pencil:

So pencil costs . Now we need to know the cost of pencils. We multiply by .

So pencils cost .

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:

- Question
Jenny buys felt-tip pens. It costs her . How much would pens have cost?

The answer is .

You divide by , then multiply the answer by .

- pens cost
- pen costs (or pence)
- So pens would cost