3.4

## National STEM Learning Centre

Skip to 0 minutes and 0 seconds[Michael] In this video, we explore the approximate conversion between miles and kilometres using three different examples. Eight kilometres is approximately the same as five miles. A sign shows that the distance to Paris is 32 kilometres. How far is that in miles? By setting up a proportion diagram, it is easy to see that the number of kilometres has to be multiplied by four. The multiplier from kilometre to miles is not given since it would involve a decimal. Part of working with proportion is realising which multiplier makes the calculation easiest. 5 miles multiplied by 4 equals 20 miles. In this example, we compare speeds measured in kilometres per hour with those measured in miles per hour.

Skip to 0 minutes and 57 secondsA speed limit sign shows 70 miles per hour. A car is travelling at 96 kilometres per hour. The driver wants to know if they are within the speed limit. Convert 96 kilometres per hour in to miles per hour. In the proportion diagram, the number of kilometres has been multiplied by 12. The number of miles must also be multiplied by 12. The speed is 60 miles per hour. The car is travelling within the speed limit. In this final example, we are going to convert miles into kilometres. A sign shows the distance to London is 35 miles. How many kilometres is it to London? The number of miles has been multiplied by seven.

Skip to 1 minute and 48 secondsSo the number of kilometres must also be multiplied by seven. The distance to London is 56 kilometres. The numbers in this question were deliberately chosen to give whole number answers. In the next section, you will see how to use a conversion graph for numbers that don't work out in such a straightforward way.

# Approximate conversion of units

In this video we apply the techniques encountered so far in this course to problems where we are converting between different units.

For these problems, students should be made aware that 5 miles is approximately equal to 8 kilometres. This piece of information can be used to convert between miles and kilometres and also between a speed give in miles per hour to the same speed expressed in kilometres per hour.

This is possible as the distance travelled in miles and the distance travelled in km is proportional.

## Problem sheet

Watch the video then attempt questions 4, 5 and 6 on this week’s worksheet.