Convert Ratio to Proportional Scale with Mixed Units

In this activity, we will be changing ratio given in different units into a proportional ratio in one scale. 

We use a proportional scale when we produce a scale drawing. 

We would need a scale drawing in order to produce anything from toy cars being a scale model of actual cars, to high rise buildings having models made before being built.

The scale in a scale drawing is often shown as a ratio.

A ratio of 1:100 means that 1 cm on the drawing represents 100 cm in actual real life.

This could also be written as 1 cm:1 m or 1 cm to 1 m.

This means that a scale of 1 cm to 5 m would be written as 1:500 because there are 100 cm in one metre.

That is 1 cm: 500 cm when converted to the same units.

The scale on maps is written in this form.

Let's have a look at a conversion.

Example

On a map, 1 cm represents 2 km. The map maker has to convert this to a proportional ratio.

How would this be written?   

Answer

The ratio is 1 cm to 2 km

We know:

10 mm = 1 cm

100 cm = 1 m

1,000 m = 1 km

To change 2 km to cm we need to multiply by 1,000 to get m and then multiply by 100 to get cm.

2 km x 1,000 x 100 = 200,000 (two hundred thousand)

Answer = 1 : 200,000

Let's try some questions like this!