Ratio, Proportion & Rates of Change
Grade 3-5Conversion Graphs
A conversion graph is a straight line that lets you switch between two units, such as miles and kilometres or pounds and dollars, without doing a calculation, just by reading across from one axis to the other. This lesson covers reading a value from a conversion graph, finding the conversion rate from the graph, and using the graph to solve problems that combine or compare converted amounts.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Reading a value from a conversion graph
Find the known value on one axis, draw a line up or across to meet the graph line, then draw a line across or down to the other axis and read off the converted value.
On a graph converting miles to kilometres, 50 miles lines up with 80 km. To convert 30 miles, find 30 on the miles axis, trace up to the line, then across to the kilometres axis.
Finding the conversion rate from the graph
Pick a point on the line, usually where it crosses a clear gridline, and divide the value on one axis by the matching value on the other axis to find how much one unit is worth.
If 50 miles equals 80 km on the graph, the conversion rate is 80 ÷ 50 = 1.6, so 1 mile is equal to 1.6 km.
Using the graph for combined problems
When a question involves more than one amount, convert each amount separately using the graph, then add, subtract or otherwise combine the converted values.
A journey covers 20 miles then 15 miles. Reading the graph, 20 miles converts to 32 km and 15 miles converts to 24 km, so the total distance is 32 + 24 = 56 km.
Using the graph to compare two quantities
To compare two quantities given in different units, convert them both to the same unit using the graph, then compare the converted values directly.
A runner in the UK covers 25 miles, and a runner in France covers 45 km. Converting 25 miles using the graph gives 40 km, which is less than 45 km, so the runner in France went further, by 5 km.
Worked Examples
Three exam-style questions, fully solved.
A conversion graph shows that 50 miles is equal to 80 km. Use the graph to convert 30 miles to kilometres.
Easy- 1.Find the conversion rate: 80 ÷ 50 = 1.6 km per mile
- 2.Multiply the given distance by the rate: 30 × 1.6
Answer: 48 km
Maria has £16, which the graph shows is equal to $20. She spends $10 while abroad. Use the graph to find how much she has left, in pounds.
Medium- 1.Convert £16 to dollars using the graph: £16 = $20
- 2.Subtract the amount spent: $20 − $10 = $10
- 3.Convert $10 back to pounds using the graph: $10 = £8
Answer: £8
A runner in the UK covers 25 miles. A runner in France covers 45 km. The graph shows that 25 miles is equal to 40 km. Use the graph to find who ran further, and by how much.
Hard- 1.Convert 25 miles to kilometres using the graph: 25 miles = 40 km
- 2.Compare this to the distance run in France: 45 km is more than 40 km
- 3.Find the difference: 45 − 40 = 5 km
Answer: The runner in France went further, by 5 km
Avoid These
The most common mistakes students make.
Reading the axes the wrong way round, converting in the opposite direction to the one the question asks for.
Misreading the scale on an axis, especially when the gridlines do not go up in simple steps like 1s or 10s.
Forgetting to convert both quantities into the same unit before comparing or combining them.
Finding the conversion rate by dividing the two axis values the wrong way round.
In multi-step problems, forgetting to convert back to the original unit at the end, leaving the answer in the wrong currency or unit.
FAQ
Questions parents and students ask.
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