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11.2 Using Ratios 1

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

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: equivalent ratios, finding a missing amount, and scaling mixtures and recipes. 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

  • Make equivalent ratios by multiplying or dividing every part by the same number
  • Find a missing amount when you know a ratio and one of the amounts
  • Scale mixtures and recipes that are given as a ratio
  • Find a total when you know a ratio and one amount

Key words

  • Equivalent ratios: Ratios that describe the same comparison, for example 3 : 4, 6 : 8 and 30 : 40.
  • Scale factor: The number you multiply every part by to go from one ratio to an equivalent one.
  • Ratio table: A table with one column for each part, where every row is an equivalent ratio.
  • Mixture: Two or more things combined in a fixed ratio, such as paint, mortar or squash.

Equivalent ratios

Multiply or divide every part by the same number and the ratio stays the same. Adding the same number to each part does not work.

Worked example: a missing number

Find the missing number: 3 : 4 = ? : 20
4 → 20 is × 5, so multiply the other part by 5 too: 3 × 5 = 15

Answer: 3 : 4 = 15 : 20

Finding a missing amount

If you know the ratio and one of the amounts, find the scale factor (or the value of one part) and use it for the other amount.

Worked example: mortar

Mortar is made from sand and cement in the ratio 5 : 2. A builder uses 30 kg of sand. How much cement does she need?
5 parts = 30 kg, so 1 part = 30 ÷ 5 = 6 kg.
Cement = 2 parts = 2 × 6 = 12 kg.

Answer: 12 kg of cement

Recipes and mixtures

A ratio table keeps track when you scale up. Each row is the ratio multiplied by the same number.

  • Ratio; Flour (g) 6; Butter (g) 3; Sugar (g) 2
  • × 25; Flour (g) 150; Butter (g) 75; Sugar (g) 50
  • × 75; Flour (g) 450; Butter (g) 225; Sugar (g) 150

Worked example: a three-part recipe

Shortbread uses flour, butter and sugar in the ratio 6 : 3 : 2. Mo has 450 g of flour. How much butter and sugar does he need?
6 parts = 450 g, so 1 part = 450 ÷ 6 = 75 g.
Butter = 3 × 75 = 225 g. Sugar = 2 × 75 = 150 g.

Answer: 225 g butter and 150 g sugar

Worked example: squash

Orange squash is mixed with water in the ratio 1 : 6. How much water goes with 250 ml of squash?
Scale factor = 250. Water = 6 × 250 = 1500 ml = 1.5 litres.

Answer: 1500 ml (1.5 litres)

Finding the total

Once you know the value of one part, the total is (number of parts) × (value of one part).

Worked example: a youth club

In a youth club the ratio of boys to girls is 4 : 5. There are 32 boys. How many children are in the club?
4 parts = 32, so 1 part = 8. Total parts = 4 + 5 = 9.
Total = 9 × 8 = 72. (Girls = 5 × 8 = 40; check 32 + 40 = 72 ✓)

Answer: 72 children

Key fact: Use the part you know to find one part. Then you can find any other part or the total.

Common mistakes

  • Adding instead of multiplying: 2 : 3 is not equivalent to 4 : 5.
  • Matching the amount to the wrong part. If 30 kg is sand, it goes with the sand part (5), not the cement part.
  • Dividing by the total number of parts when you were given only one part, not the total.
  • Forgetting units, or mixing ml and litres in the same answer.

Revision questions

Try these, then check your answers below each one.

Question 1. Find the missing number: 3 : 8 = 12 : ?

Answer: 32

Working: 3 × 4 = 12, so 8 × 4 = 32.

Question 2. Which ratio is equivalent to 5 : 2? (Choose from: 10 : 4, 7 : 4, 15 : 5, 5 : 20.)

Answer: 10 : 4

Working: 5 × 2 = 10 and 2 × 2 = 4, so 10 : 4.

Question 3. Mortar is made from sand and cement in the ratio 4 : 1. A builder uses 36 kg of sand. How much cement does he need?

Answer: 9 kg

Working: 1 part = 36 ÷ 4 = 9 kg. Cement is 1 part = 9 kg.

Related lessons

Continue in the full course

This lesson is section 11.2 (EGCMF1102) 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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