Ratio, Proportion & Rates of Change
Grade 5-6Ratio and Fractions
Ratios and fractions describe the same kind of information in two different ways, and being able to switch between them is essential for GCSE Maths. This lesson covers converting a ratio into a fraction, converting a fraction into a ratio, and combining ratios and fractions to solve problems where part of a quantity changes.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Converting a ratio to a fraction of the whole
Add the parts of the ratio to find the total number of parts, then write each part as a fraction with this total as the denominator.
The ratio of boys to girls in a class is 3:5. The total number of parts is 3 + 5 = 8, so girls make up 5/8 of the class.
Converting a ratio to a fraction of another part
When a question asks for one quantity as a fraction of another, rather than of the whole, write the ratio directly as a fraction using only those two parts, without adding them together.
The ratio of cats to dogs is 2:7. The number of cats is 2/7 of the number of dogs, not 2/9, since the question compares cats to dogs, not cats to the total number of animals.
Converting a fraction to a ratio
Find the remaining fraction by subtracting the given fraction from 1, write the two fractions as a ratio, then simplify by multiplying or dividing to clear the denominators.
In a bag of sweets, 2/5 are red and the rest are blue. The blue fraction is 1 − 2/5 = 3/5, so the ratio is 2/5 : 3/5, which simplifies to 2:3.
Finding a new ratio after part of a quantity changes
Use the given ratio to find the actual amount of each part, apply the fraction that describes the change to work out the new amount, then write and simplify the new ratio.
The ratio of red to blue counters is 3:5, with 12 red counters, so there are 12 ÷ 3 × 5 = 20 blue counters. Removing 1/3 of the red counters leaves 12 − 4 = 8 red counters, giving a new ratio of 8:20, which simplifies to 2:5.
Worked Examples
Three exam-style questions, fully solved.
The ratio of boys to girls in a class is 3:5. What fraction of the class are girls?
Easy- 1.Find the total number of parts: 3 + 5 = 8
- 2.Write the girls' part as a fraction of the total: 5/8
Answer: 5/8
The ratio of red to blue counters in a bag is 3:5. There are 12 red counters. 1/3 of the red counters are removed. Find the new ratio of red to blue counters.
Medium- 1.Find the number of blue counters: 12 ÷ 3 × 5 = 20
- 2.Find the number removed: 1/3 × 12 = 4
- 3.Find the new number of red counters: 12 − 4 = 8
- 4.Write and simplify the new ratio: 8:20 = 2:5
Answer: 2:5
At a concert, the ratio of adults to children is 1:5. 3/8 of the children are under 10. If there are 24 adults, how many children are under 10?
Hard- 1.Find the number of children: 24 × 5 = 120
- 2.Find the fraction of children under 10: 3/8 × 120
Answer: 45 children
Avoid These
The most common mistakes students make.
Using the total number of parts as the denominator when the question asks for a fraction of just one other part, rather than of the whole.
Forgetting to find the remaining fraction, 1 minus the given fraction, before converting a fraction into a ratio.
Not fully simplifying the final ratio, leaving an answer like 8:20 instead of 2:5.
When part of a quantity changes, recalculating the ratio using the original amount instead of the new amount after the change.
Mixing up which part of the ratio corresponds to which quantity when working with real-world contexts, such as teachers and students or adults and children.
FAQ
Questions parents and students ask.
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