Practise simplifying ratios, sharing quantities and connecting ratios to fractions. Each example includes full working, with follow-on workouts and a teacher worksheet builder.
Foundation and Higher · Useful for students strengthening core skills before mixed GCSE practice.
Core pathway. Core GCSE methods are useful across Foundation and Higher. Start with the core examples and questions.
Higher extension. More demanding selections are marked Higher extension: practice question 8. Use these after the core work, following your teacher’s guidance.
4 worked examples and 8 original practice questions · Allow 35–50 minutes · Read online or print. Higher extensions are labelled. No account or email needed.
Printing includes the method, examples and space for working, followed by a separate answer section.
The fraction represented by one share uses all the parts in its denominator. In a ratio a : b, the first share is a out of a + b parts.
Read each line of working and explain why it follows from the previous line.
Convert both quantities to the same units, then divide both ratio entries by a common factor.
Writing and Simplifying Ratio · Core GCSE skill · No calculator · 2 marks
Write down the ratio 45 cm : 1.5 m in its simplest form.
Now practise this method: Question 1 · Question 2
Add all the parts, divide the total by that number, then multiply by each share. Check that the shares add back to the total.
Ratio · Core GCSE skill · No calculator · 3 marks
Amir, Bella and Carl share £132 in the ratio 1 : 4 : 6.
Work out how much money each of them gets.
Now practise this method: Question 3 · Question 4
Match the known quantity to its own number of ratio parts. Find one part, then scale to the combined number of parts. If the difference between shares is given, match it to the difference in ratio parts. To combine two ratios, first scale them so their common quantity has the same number of parts.
Ratio · Core GCSE skill · Calculator allowed · 2 marks
In a gym class, the ratio of the number of men to the number of women is 4 : 5.
There are 20 men in the class.
Work out the total number of people in the class.
Now practise this method: Question 5 · Question 6
The denominator counts all parts. In a ratio a:b, the first share is a/(a+b) of the total.
Writing a Ratio as a Fraction or Linear Function · Core GCSE skill · Calculator allowed · 2 marks
A box contains red, blue and green pens in the ratio 2 : 3 : 7.
Find the fraction of the pens that are blue. Give your fraction in its simplest form.
Now practise this method: Question 7 · Question 8
Write your working on paper. Marks indicate how much working to show; these questions are self-marked and do not change saved practice results. Use squared paper for drawing questions.
Writing and Simplifying Ratio · Core GCSE skill · No calculator · 1 marks
Write down the ratio 20 : 35 in its simplest form.
Writing and Simplifying Ratio · Core GCSE skill · No calculator · 2 marks
In a choir there are 16 sopranos and 24 altos.
Write down the ratio of the number of sopranos to the number of altos.
Give your ratio in its simplest form.
Ratio · Core GCSE skill · Calculator allowed · 3 marks
Each month Tom is paid £1800.
He saves 20% of the £1800.
He splits the rest between rent and bills in the ratio 5 : 3.
Work out how much Tom spends on rent each month.
Ratio · Core GCSE skill · Calculator allowed · 4 marks
A shop orders 240 candles.
The ratio of large candles to small candles ordered is 3 : 5.
Each large candle costs £4.20.
Each small candle costs £2.50.
Work out the total cost of the order.
Ratio · Core GCSE skill · Calculator allowed · 3 marks
In a fruit bowl there are apples, bananas and pears.
The ratio of apples to bananas is 3 : 2.
The ratio of bananas to pears is 4 : 3.
There are 24 apples in the bowl.
Work out the number of pears in the bowl.
Ratio · Core GCSE skill · Calculator allowed · 4 marks
Ella, Fred and Grace share some money in the ratio 3 : 5 : 8.
Grace gets £35 more than Ella.
Work out the total amount of money they share.
Writing a Ratio as a Fraction or Linear Function · Core GCSE skill · Calculator allowed · 2 marks
In a drama club, the ratio of the number of boys to the number of girls is 4 : 5.
Write down the fraction of the club members who are boys.
Writing a Ratio as a Fraction or Linear Function · Higher extension · Calculator allowed · 3 marks
A bag contains only red, blue and yellow counters.
The numbers of red, blue and yellow counters are in the ratio 2 : 3 : x.
A counter is taken at random from the bag.
The probability that it is yellow is .
Work out the value of x.
Compare the reasoning as well as the final answer. Another correct method is valid. If a step is unclear, revisit an example before trying a similar question.
Workouts provide interactive practice; choose the tier your school has recommended.
A bar model can help pupils explain what one part represents. Ask them to label the total and the separate shares before doing arithmetic.
Build a custom classroom worksheet or print this page. The teacher builder can display questions on a projector and reveal answers separately.