Pearson Edexcel · GCSE · Mathematics
Course version: 1MA1 · Version from Mar 2026
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
The phrase "A as a fraction of B" means A/B, so the quantity that follows the word "of" goes on the bottom.
Checked against the Pearson Edexcel 1MA1 specification (opens in a new tab) on .
- Point 3 of 18
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The phrase "A as a fraction of B" means A/B, so the quantity that follows the word "of" goes on the bottom. Put both quantities into the same unit first, then write the fraction and cancel it. For example 45 minutes as a fraction of 2 hours is 45/120, which cancels to 3/8. When the first quantity is the larger one the answer is greater than 1, and that is correct rather than a mistake: 2 hours as a fraction of 45 minutes is 120/45, which cancels to 8/3. Leave it as an improper fraction unless the question asks for a mixed number. The comparison is often hidden in wording such as "what fraction of the class", so decide which quantity is the whole before you write anything.
What earns the marks
- Converting both quantities into the same unit before the fraction is formed.
- The fraction written the right way round, with the quantity named after "of" as the denominator.
- Dividing both numbers by a common factor, even where the cancelling is not taken all the way.
- The fraction in its simplest form, which is greater than 1 whenever the first quantity is the larger of the two.
Common mistakes and how to put them right
Writing the fraction upside down, so 20 g as a fraction of 50 g is given as 50/20.
Comparing 30 cm with 2 m without converting, giving 30/2 rather than 30/200.
Assuming an answer above 1 must be wrong and inverting it to force a proper fraction.
Cancelling part way and stopping at a fraction that still has a common factor.
Exam tips
- Underline the words that come after "of"; that quantity is the denominator every time.
- Convert the units before you write the fraction, so the one you cancel is already the right one.
- Leave the answer as a fraction unless the question asks for a decimal or a percentage.
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 bag contains 3 red counters and 7 blue counters. What fraction of the counters are red?
Listen
The phrase "A as a fraction of B" means A/B, so the quantity that follows the word "of" goes on the bottom. Put both quantities into the same unit first, then write the fraction and cancel it. For example 45 minutes as a fraction of 2 hours is 45/120, which cancels to 3/8. When the first quantity is the larger one the answer is greater than 1, and that is correct rather than a mistake: 2 hours as a fraction of 45 minutes is 120/45, which cancels to 8/3. Leave it as an improper fraction unless the question asks for a mixed number. The comparison is often hidden in wording such as "what fraction of the class", so decide which quantity is the whole before you write anything. A strong answer earns marks for these points. converting both quantities into the same unit before the fraction is formed. the fraction written the right way round, with the quantity named after "of" as the denominator. dividing both numbers by a common factor, even where the cancelling is not taken all the way. the fraction in its simplest form, which is greater than 1 whenever the first quantity is the larger of the two. Exam tip: Underline the words that come after "of"; that quantity is the denominator every time.
Key words
Say what each word means before you turn the card.
fraction of a quantity
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consistent units
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improper fractions
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comparing quantities
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See every definition
- fraction of a quantity
- Writing one quantity as a fraction of another means putting the quantity named after the word "of" on the bottom.
- consistent units
- Both quantities must be put into the same unit before the fraction is written and cancelled.
- improper fractions
- An answer greater than 1 is left as an improper fraction unless the question asks for a mixed number.
- comparing quantities
- The comparison is often hidden in wording such as "what fraction of the class", so decide which quantity is the whole before writing anything.
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