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Conversion graphs

Conversion graphs

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Proportion


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Explainer Video

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Tutor: Toby

Summary

Conversion graphs

​​In a nutshell

Conversion graphs are a tool to convert between units, like between measurements for example. To read them, you just need to know how to read a straight line graph.



Converting using a graph

​​procedure

1.
Given a conversion graph that converts between unit X on the xx-axis and unit Y on the yy-axis, decide whether you want to convert from X to Y or Y to X.​
2a.
If converting from X to Y, read the X value off the xx-axis and find the corresponding yy-coordinate on the graph. This is the Y value converted from the X value.​
2b.
If converting from Y to X, read the Y value off the  yy-axis and find the corresponding xx-coordinate on the graph. This is the X value converted from the Y value. ​



Converting currencies

An example of a conversion graph is given below. It shows the relationship between two currencies, pounds sterling and euros.


Example 1

Use the graph below to convert £30£30 into euros.

Maths; Other graphs; KS3 Year 7; Conversion graphs


You are converting from pounds to euros. Since pounds is on the xx-axis, go from x=30x=30 up to the line, then across to read the in-line value on the yy-axis. This is approximately y=35y=35. Hence 

£30£30​ is approximately 35\underline{€35}


Example 2

Use the same currency conversion graph to convert 50€50 into pounds sterling.


To convert from euros to pounds, start on the yy-axis, and find the corresponding xx-coordinate. Start at y=50y=50 on the yy-axis, go across until you meet the line, then go down to see the value on the xx-axis that is in-line. 


This is approximately 4242, so

50€50 is about £42\underline{£42} 


Note: The word "approximately" is used because the exact point is not labelled on the axis, so it can be tricky to read the exact value.



Converting distances

Converting distances on a conversion graph works in the exact same way as converting currencies.


Example 3

The graph below shows conversions between miles and kilometres:

Maths; Other graphs; KS3 Year 7; Conversion graphs


Find how many kilometres there are in five miles. 


Go to five on the miles axis (the yy-axis) and trace across until you meet the straight line graph. Then trace down to the kilometres axis (the xx-axis). It reads approximately 88, so you have found that five miles is about eight kilometres.



​​The gradient

The gradient of the straight line in a conversion graph represents how to convert one of the xx-unit into yy-units. Namely, if the gradient is mm​, then one of the xx-unit is mm of the yy-units.​

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Exercises

FAQs - Frequently Asked Questions

How do you read a conversion graph?

What does the gradient of a conversion graph line represent?

What are conversion graphs?

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