# Writing and Simplifying Ratio

## Writing Ratio

We use ratio to compare amounts.

Here are some red squares and some blue squares.

There are 3 red squares and 6 blue squares.
We can say the ratio of red to blue squares is 3:6
We read this as 3 to 6
For every 3 red squares, there are 6 blue squares.

3 and 6 are both in the 3 times table so we can simplify this ratio by dividing both numbers by 3
The ratio of red squares to blue squares is 1:2

If we wanted to write the ratio of blue squares to red squares we would have to write the numbers the other way around.
The ratio of blue squares to red squares is 6:3 or simplified it is 2:1

Here are some yellow circles, some blues circles and some red circles

There are 4 yellow circles, 2 blue circles and 6 red circles. The ratio of yellow circles to blue circles to red circles is 4:2:6

4, 2 and 6 are all in the 2 times table so we can simplify by dividing by 2
The ratio of yellow circles to blue circles to red circles is 2:1:3

Try this:

Write the ratio of red rings to blue rings.

## Simplifying Ratio

We simplify ratio in the same way we simplify fractions.

Simplify 10:15

10 and 15 are both in the 5 times table, we can simplify by dividing both 10 and 15 by 5

10 ÷ 5 = 2
15 ÷ 5 = 3

10:15 = 2:3

Simplify 20:8

20 and 8 are both in the 4 times table (they are also both in the 2 times table), we can simplify by dividing both 20 and 8 by 4

20 ÷ 4 = 5
8 ÷ 4 = 2

20:8 = 5:2

If we had divided by 2 we would get 10:4
To simplify fully we would have to divide by 2 again - we would then get the same answer 5:2

Try these:

## Converting between a fraction and a ratio

Example: 15 of pens in a box a green, the rest are red. Write the ratio of green pens to red pens.

A whole is 55

5515 = 45

45 of the pens are red

Out of every 5 pens, 1 is green and 4 are red

The ratio of green pens to red pens is 1:4

Example: The ratio of black pens to blue pens in a box is 3:1
What fraction of the pens are black?

For every 3 black pens there is 1 blue pen
Out of every 4 pens 3 are black.

34 of pens are black

Try these: