Proportion
Practise proportion with this free Foundation GCSE Maths worksheet from Virtus Academy. You'll work through direct and inverse proportion, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. Use the unitary method: find one, then find many.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
Proportion describes how two quantities relate as a fraction of a whole, or how they change together. It is closely linked to ratio, fractions and percentages.
If a class of \(30\) has \(12\) girls, the proportion of girls is \(\frac{12}{30}\), which simplifies to \(\frac{2}{5}\) or \(40\%\). Proportion compares a part with the whole, whereas ratio compares parts with each other.
That distinction is worth holding onto. In a class with \(12\) girls and \(18\) boys, the ratio is \(12 : 18 = 2 : 3\), but the proportion of girls is \(\frac{2}{5}\). Both describe the same class, but they answer different questions.
Revision notes
Proportion as part of the whole
Write the part over the total, then simplify or convert to a percentage.
For \(9\) red counters out of \(20\), the proportion is \(\frac{9}{20}\), which is \(0.45\) or \(45\%\).
Proportion versus ratio
Ratio compares parts with each other; proportion compares a part with the whole.
With \(4\) cats and \(6\) dogs, the ratio is \(2 : 3\) but the proportion of cats is \(\frac{4}{10} = \frac{2}{5}\).
Scaling recipes and quantities
If quantities are in proportion, multiplying one by a scale factor means multiplying them all.
Doubling a recipe doubles every ingredient. Working out the scale factor first, then applying it to each quantity, is the reliable method.
Key points
- Proportion compares a part with the whole.
- Ratio compares parts with each other.
- Write the part over the total.
- Simplify or convert to a percentage.
- Scaling in proportion multiplies every quantity.
- Find the scale factor before applying it.
Worked examples
Example 1
A bag has \(7\) red and \(13\) blue counters. Find the proportion that are red.
Working
Example 2
In a group of \(24\), \(9\) wear glasses. Express this as a proportion in its simplest form.
Working
Example 3
A recipe for \(4\) people uses \(200\)g of rice. How much is needed for \(10\) people?
Working
Common mistakes
Using one part rather than the total as the denominator.
With 7 red and 13 blue, the proportion of red is 7/20, not 7/13.
Confusing proportion with ratio.
Ratio compares the parts; proportion compares a part with the whole.
Scaling only some quantities.
In proportion, every quantity must be multiplied by the same scale factor.
Leaving the fraction unsimplified.
9/24 should be given as 3/8 when the simplest form is wanted.
Exam tips
- Work out the total before writing the proportion.
- Decide whether the question wants a proportion or a ratio.
- Find the scale factor first when scaling quantities.
- Simplify fractions and check percentages are under 100.
Key terms
- Proportion
- A part expressed as a fraction of the whole.
- Ratio
- A comparison between parts.
- Scale factor
- The number every quantity is multiplied by.
- Simplest form
- A fraction reduced to its smallest whole numbers.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.