# Ratio and proportion

In this lesson, you'll learn about ratio and proportion.

Let's get started straight away. First consider ...

## ... what is a ratio?

It's a way of showing the relationship between two or more quantities.

## Examples of ratios

Say you have two red counters and one green counter

 •• •

The ratio of red to green counters is two to one and can be expressed

2  :  1

## Now consider another ratio and proportion

Take a close look at four red and two green counters

 •••• ••

In this case the ratio of red to green counters is

4  :  2

Notice in both the above examples for every two red counters there's one green counter.

In other words, the ratios 2 : 1 and 4 : 2 are equal to each other and proportion is a statement of this equality.

## How about three red, two green and one blue counter?

 ••• •• •

The ratio of red to green to blue counters is three to two to one

3  :  2  :  1

## And what about six red, four green and two blue counters?

 •••••• •••• ••

Here the ratio of red to green to blue counters is

6  :  4  :  2

Can you see that for every three red counters, there are two green counters and one blue counter? This also applies to the 3 : 2 : 1 ratio above.

i.e. our example ratios 3 : 2 : 1 and 6 : 4 : 2 are equal to each other.

## Ratios and fractions

Let's go back to our original ratio two red counters to one green counter

 •• •

2  :  1

There are three counters altogether.

Two of these three counters are red, so the fraction of counters which are red is

2 / 3

- two thirds.

One of these three counters is green, making the fraction of counters which are green

1 / 3

- one third.

## Have a go yourself!

In each case, write down the ratio and work out the fraction of counters which are red. The ratio of red to green counters is

1  :  5

There are six counters altogether - one of these is red, so the fraction of counters which are red is

1 / 6

- one sixth. Here the ratio of red to green to blue counters is

1  :  5  :  3

Given there are nine counters altogether and one's red, the fraction of counters which are red is

1 / 9

- one ninth.

## How did you do?

Hopefully you now have a basic grasp of ratio and proportion, and ratios and fractions. Try varying the number of colored counters and make up your own ratios!

Have you checked out the following topics yet?

Fractions

Percentages