AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Express one quantity as a fraction of another, where the fraction is less…
Full specification wording
Ratio, proportion and rates of change: express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
To express one quantity as a fraction of another, write the first quantity as the numerator and the second as the denominator, then simplify.
Checked against the AQA 8300 specification (opens in a new tab) on .
- Point 4 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
To express one quantity as a fraction of another, write the first quantity as the numerator and the second as the denominator, then simplify. The fraction may be less than 1 or greater than 1. For example, 15 as a fraction of 40 is 15/40 = 3/8, which is less than 1. For example, 50 as a fraction of 20 is 50/20 = 5/2, which is greater than 1. Quantities must be in the same unit before forming the fraction; convert first, then simplify by dividing numerator and denominator by their highest common factor. The denominator must be the quantity being compared with, so read the wording carefully to decide which quantity goes on the bottom.
What earns the marks
- Write the first named quantity as the numerator and the second as the denominator.
- Convert both quantities to the same unit before forming the fraction.
- Simplify the fraction by dividing numerator and denominator by their highest common factor.
- Recognise that the resulting fraction may be less than 1 or greater than 1.
- Interpret the fraction correctly in context, for example as a proportion of a total.
Common mistakes and how to put them right
Reversing the fraction: writing 40/15 instead of 15/40 when expressing 15 as a fraction of 40.
Put it right by putting the first quantity on top and the second on the bottom.
Forgetting to convert units.
Put it right by converting both to the same unit first.
Leaving the fraction unsimplified when a simplified form is expected.
Put it right by dividing numerator and denominator by their highest common factor.
Assuming the answer must be less than 1.
Put it right by allowing fractions greater than 1 when the first quantity is larger than the second.
Exam tips
- Underline the two quantities and the word 'of' to identify numerator and denominator before writing the fraction.
- Convert to the smaller unit first so both quantities are whole numbers where possible.
- Check whether the fraction should be less than or greater than 1 by comparing the sizes of the two quantities.
Try the lesson
The start of the Ratio, proportion and rates of change: express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1 lesson, made from checked teaching notes for this specification point.
Have a go first
A class has 7 girls and 12 boys. Express the number of girls as a fraction of the number of boys. Give your answer in its simplest form.
Listen
To express one quantity as a fraction of another, write the first quantity as the numerator and the second as the denominator, then simplify. The fraction may be less than 1 or greater than 1. For example, 15 as a fraction of 40 is 15/40 = 3/8, which is less than 1. For example, 50 as a fraction of 20 is 50/20 = 5/2, which is greater than 1. Quantities must be in the same unit before forming the fraction; convert first, then simplify by dividing numerator and denominator by their highest common factor. The denominator must be the quantity being compared with, so read the wording carefully to decide which quantity goes on the bottom. A strong answer earns marks for these points. Write the first named quantity as the numerator and the second as the denominator. Convert both quantities to the same unit before forming the fraction. Simplify the fraction by dividing numerator and denominator by their highest common factor. Recognise that the resulting fraction may be less than 1 or greater than 1. A common slip: Reversing the fraction: writing 40/15 instead of 15/40 when expressing 15 as a fraction of 40. Instead, putting the first quantity on top and the second on the bottom. Exam tip: Underline the two quantities and the word 'of' to identify numerator and denominator before writing the fraction.
Watch it explained
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Read the described scene instead
This lesson shows how to express one quantity as a fraction of another. You will write the first quantity as the numerator and the second as the denominator. The result can be less than one or greater than one. We will also check units and simplify. The word 'of' tells you which quantity goes underneath. For '15 as a fraction of 40', 15 is the numerator and 40 is the denominator, giving 15 over 40. Read the wording carefully so you do not reverse the fraction. Follow three steps. Write the first named quantity over the second. If the units differ, convert both to the same unit before forming the fraction. Then simplify by dividing numerator and denominator by their highest common factor. Let's work through 15 as a fraction of 40. Write 15 over 40. Pause and try simplifying before I continue. The highest common factor of 15 and 40 is 5. Divide both by 5 to get 3 over 8, which is less than 1. Now express 50 as a fraction of 20. Write 50 over 20. Pause and simplify. The highest common factor of 50 and 20 is 10. Dividing both by 10 gives 5 over 2, which is greater than 1. Watch for four common mistakes. Reversing the fraction: 15 as a fraction of 40 is 15 over 40, not 40 over 15. Forgetting units: compare 30 centimetres with 2 metres as 30 over 200, not 30 over 2. Leaving the fraction unsimplified when a simplified form is expected. Assuming the answer must be less than 1; it can be greater when the first quantity is larger. To recap: identify the two quantities and underline the word 'of'. Write the first as the numerator and the second as the denominator. Convert to the same unit, using the smaller unit where possible, then simplify by the highest common factor. Check whether your fraction should be less than or greater than 1 by comparing the two quantities.
Key words
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Fraction notation and simplification
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Comparing quantities of the same kind
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Unit conversion before comparison
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Fractions greater than 1 as improper fractions
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See every definition
- Fraction notation and simplification
- Writing the first quantity as the numerator and the second as the denominator, then dividing numerator and denominator by their highest common factor.
- Comparing quantities of the same kind
- The denominator must be the quantity being compared with, so read the wording carefully to decide which quantity goes on the bottom.
- Unit conversion before comparison
- Quantities must be in the same unit before forming the fraction; convert first, then simplify.
- Fractions greater than 1 as improper fractions
- The fraction may be less than 1 or greater than 1, so allow fractions greater than 1 when the first quantity is larger than the second.
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