A lot of the time, it's not really the best idea to have things full size. A map would be useless if it was full size, a toy car doesn't really want to be the same size as a normal car.

When we have this issue, we use a scale diagram or a scale model.

**What is a scale ****diagram?**

A scale diagram is just a diagram where everything has been reduced by the same factor, it could be half the size, a tenth of the size or anything else.

**How are scales written?**

Scales are written as a ratio such as 1: 100 or 1:50 000

**What does this mean:?**

Scales are read left to right. The scale 1:100, for example, would mean that every 1 unit of **length** on the scale is the same as 100 units in real life.

So something that was 2 cm long in real life would be 200 cm long in real life.

**Example 1: A model car is 3m tall. If the scale is 1:100, how tall would the model car be?**

We know that there is a factor of 100 and that the model is smaller

All we need to do here is change the units into cm and divide by the scale factor.

300 ÷ 100 = 3 cm

**Example 2: A model is made of a 2 m tall man. If the model is 4 cm tall, what is the scale?**

The first thing we should notice here is that the units are different, so we need to make them the same.

2m = 200 cm

Step 2 is to write these numbers as a ratio (remember the model comes first))

4:200

Out third and final step is to simplify this ratio.

1:50