One of the most common applications for ratio is using them for map scales.

Normally ratios are given as two numbers (for example 1:5000) where both numbers must have the same units.

For map scales, because the numbers are usually quite large, they can be given with different units.

Examples of map scales may look like this 1:25k, 1:50k (These are the two that are used for ordanance survey maps) or something along the lines of 1cm:5miles

1 : 25k would mean that every 1 cm on the map would be 25000 cm in real life. 1 cm : 5 miles would mean 1cm represents 5 miles in real life.

**Example 1:**

A map has a scale of 1:25k. If a river was 2cm long on the map, how long would it be in real life.

Step 1: Write the ratio out in full

1 : 25 000

Step 2: Write in the information you know under this.

1 : 25 000

2: x

Step 3: Look at the numbers you know (the 1 and 2) and work out the realtionship (In this case, it is multiply by 2) and so the same to the other side of the ratio.

1 : 25 000

2: 50 000

This means the river is 50 000 cm long in real life.

**Example 2: **

Two car parks are 15 miles apart. If the scale for a map is 1 cm: 5 miles, How far apart are the car parks on the map?

Step 1: Write the ratio out in full

1 cm : 5 miles

Step 2: Write in the information you know under this.

1 cm : 5 miles

x : 15 miles

Step 3: Look at the numbers you know (the 5 and 15) and work out the relationship (In this case, it is multiply by 3) and so the same to the other side of the ratio.

1 cm : 5 miles

3 cm : 15 miles

This means the car parks are 3 cm apart on the map