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11.4 Using Ratios 2

GCSE Maths Foundation · Edexcel · Chapter 11: Ratio and Proportion

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: sharing in a ratio, ratios and fractions, and problems using the difference between parts. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Share an amount in a ratio with two or three parts
  • Change between a part : part ratio and a fraction of the whole
  • Solve ratio problems when you know the difference between two parts
  • Solve multi-step ratio problems with money and measures

Key words

  • Part : part ratio: Compares one share with another share, such as red : blue = 3 : 5.
  • Part : whole: Compares one share with the total. With red : blue = 3 : 5 the whole is 8 parts, so red is 3/8.
  • Total parts: The sum of the numbers in the ratio. 2 : 3 : 5 has 10 parts.
  • Difference: How much bigger one share is than another. In 2 : 5 the difference is 3 parts.

Sharing in a ratio

Add the parts. Divide the amount by the total parts to find one part. Multiply by each number in the ratio. Check that the shares add back to the total.

Worked example: three people

Priya, Josh and Kemi share £120 in the ratio 2 : 3 : 5.
Total parts = 2 + 3 + 5 = 10. One part = £120 ÷ 10 = £12.
Priya 2 × £12 = £24. Josh 3 × £12 = £36. Kemi 5 × £12 = £60. Check: 24 + 36 + 60 = 120 ✓

Answer: £24, £36 and £60

Ratios and fractions

A ratio compares parts with each other. A fraction compares a part with the whole. To change a ratio into fractions, the denominator is the total number of parts.

Worked example: ratio to fraction

A bag holds red and blue beads in the ratio 3 : 5. What fraction of the beads are blue?
Total parts = 3 + 5 = 8. Blue is 5 of the 8 parts.

Answer: 5/8

Worked example: fraction to ratio

2/7 of the people in a cinema are children. The rest are adults. Write children : adults.
Children are 2 parts out of 7, so adults are 7 − 2 = 5 parts.

Answer: 2 : 5

Using the difference

Sometimes you are told how much more one person has. The difference between the numbers in the ratio tells you how many parts that is.

Worked example: ages

The ratio of Sita’s age to her dad’s age is 2 : 5. Her dad is 12 years older than Sita. How old are they?
Difference = 5 − 2 = 3 parts = 12 years, so 1 part = 4 years.
Sita = 2 × 4 = 8. Dad = 5 × 4 = 20. Check: 20 − 8 = 12 ✓

Answer: Sita is 8 and her dad is 20

Multi-step problems

Work in clear steps and label each amount. After a change, find the new amounts before you write a new ratio.

Worked example: sharing then giving

Amir and Beth share £84 in the ratio 3 : 4. Beth then gives 1/4 of her share to Amir. Write the new ratio Amir : Beth.
One part = £84 ÷ 7 = £12. Amir £36, Beth £48.
Beth gives 1/4 of £48 = £12. Amir £36 + £12 = £48, Beth £48 − £12 = £36.
New ratio 48 : 36 = 4 : 3

Answer: 4 : 3

Key fact: Total parts → one part → each share. Write the value of one part clearly: most marks come from that step.

Common mistakes

  • Dividing by one of the numbers in the ratio instead of the total number of parts.
  • Thinking 1 : 3 means 1/3. With a ratio of 1 : 3 there are 4 parts, so the first share is 1/4.
  • Treating the difference as the total. If Dad is 12 years older, 12 is 3 parts, not 7 parts.
  • Not checking that the shares add back up to the original amount.

Revision questions

Try these, then check your answers below each one.

Question 1. 96 sweets are shared in the ratio 1 : 2 : 5. How many sweets are in the largest share?

Answer: 60

Working: 8 parts. One part = 96 ÷ 8 = 12. Largest = 5 × 12 = 60.

Question 2. A tray holds red and white roses in the ratio 4 : 5. What fraction of the roses are red? (Choose from: 4/5, 4/9, 5/9, 1/4.)

Answer: 4/9

Working: 4 + 5 = 9 parts. Red is 4 of them: 4/9.

Question 3. 3/10 of the members of a gym are juniors. The rest are seniors. Write the ratio juniors : seniors.

Answer: 3:7

Working: Juniors 3 parts, seniors 7 parts: 3 : 7.

Related lessons

Continue in the full course

This lesson is section 11.4 (EGCMF1104) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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