One of the most common applications for** ratios** is using them in **map scales**.

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

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

Examples of map scales may look like this:

1:50 k > 1 cm on the map would be 50000 cm in real life

1 cm:5 miles > 1 cm represents 5 miles in real life

Let's look at these ratios in action now in some examples.

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

Step 1: Write the ratio out in full:

1:25000

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

1:25000

2: ?

Step 3: Look at the numbers you know and work out the relationship between them to apply to find the missing number:

In this case, we multiply 1 by 2 to reach 2 so our rule is '× 2'.

1:25000 × 2

2:50000

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

e.g. 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

?:15 miles

Step 3: Look at the numbers you know and work out the relationship between them to apply to find the missing number:

5 × 15 = 3 so our rule here is '× 3'.

1 cm:5 miles

3 cm:15 miles

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

In this activity, we will apply map scales to find the scale values of real life elements or the real values of scaled elements on maps.