EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Ratios
Fractions, ratio and percentages · Lesson 2 of 5
Last Lesson and Before
Answer each one, then check.
1. What is the HCF of 12 and 18?
6
2. Last lesson: work out 3/5 of 40.
24
3. Simplify 15/25.
3/5
4. How many grams are in 1.2 kg?
1200 g
Learning Objectives
1. Simplify ratios, including ratios with different units.
2. Write a ratio in the form 1 : n or n : 1.
3. Connect ratios and fractions.
4. Share an amount in a given ratio.
5. Solve ratio problems when you know the difference or one part.
What a Ratio Is
A ratio compares amounts: 3 red counters to 5 blue is written 3 : 5.
▸ The order matters. 3 : 5 (red to blue) is not the same as 5 : 3.
▸ Simplify. Divide every part by the HCF: 12 : 18 = 2 : 3.
▸ Same units first. 45 cm : 1.2 m becomes 45 : 120 (both in cm), then 3 : 8.
▸ Decimals and fractions. Multiply every part to make whole numbers: 1.5 : 2 = 3 : 4.
Simplifying with Different Units
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Write 45 cm : 1.2 m in its simplest form. |
1. Put both in the same units
1.2 m = 120 cm
2. Write the ratio in cm
45 : 120
3. The HCF of 45 and 120 is 15
45 ÷ 15 = 3, 120 ÷ 15 = 8
Answer: 3 : 8
Ratios and Fractions
A ratio tells you how many parts there are altogether.
▸ Total parts. In the ratio 3 : 5 there are 3 + 5 = 8 parts.
▸ As fractions. The first amount is ⅜ of the total and the second is ⅝.
▸ Not the same thing. 3 : 5 does NOT mean 3/5 of the total - it means ⅜.
▸ Unit ratios. Divide to make one part 1: 4 : 10 = 1 : 2.5, and 10 : 4 = 2.5 : 1.
Sharing with a Bar Model
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A bar model makes a ratio visible. The ratio 3 : 4 has 7 equal parts. £84 shared into 7 parts is £12 a part, so the shares are 3 × 12 = £36 and 4 × 12 = £48. |
7 parts share £84, so each part is £12. |
Sharing in a Ratio
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Share £84 between Amy and Ben in the ratio 3 : 4. |
1. Add the parts
3 + 4 = 7 parts
2. Find one part
84 ÷ 7 = 12
3. Multiply for each person
Amy 3 × 12 = 36, Ben 4 × 12 = 48
4. Check
36 + 48 = 84
Answer: Amy £36, Ben £48
When You Know the Difference
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The ages of a father and son are in the ratio 5 : 2. The father is 18 years older than the son. How old is each? |
1. The difference in parts
5 − 2 = 3 parts
2. 3 parts are 18 years, so one part is
18 ÷ 3 = 6
3. Multiply
Father 5 × 6 = 30, son 2 × 6 = 12
4. Check the difference
30 − 12 = 18
Answer: Father 30, son 12
Key Terms
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Ratio A comparison of the sizes of two or more quantities. |
Simplest form A ratio whose parts have no common factor other than 1. |
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Part One share of a ratio; the total number of parts is the sum of the ratio. |
Unit ratio A ratio written with one part equal to 1, such as 1 : n. |
Your Task: Ratio Problems Relay
12 minutes
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(a) Simplify 24 : 36 : 60. (b) Share 450 g of sweets in the ratio 2 : 3 : 4. (c) Paint is mixed blue to white in the ratio 2 : 7. How much white is mixed with 5 litres of blue? (d) Write 8 : 5 in the form n : 1. 1. Decide what you know: the total, one part, or a difference. 2. Find the value of one part. 3. Answer the question asked. |
A good answer shows: (a) 2 : 3 : 5 (b) 100 g, 150 g, 200 g (c) 5 ÷ 2 = 2.5 litres per part, so 7 × 2.5 = 17.5 litres (d) 1.6 : 1
Can I...?
☐ Simplify a ratio.
☐ Simplify a ratio with different units.
☐ Write a ratio as 1 : n or n : 1.
☐ Write a ratio as fractions of the total.
☐ Share an amount in a ratio.
☐ Solve problems when I know one part or the difference.
Summary
✓ Simplify by dividing every part by the HCF; use the same units first.
✓ Total parts = sum of the ratio; each share is a fraction of the total.
✓ Find the value of one part, then multiply.
✓ A difference in amounts matches the difference in parts.
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EXAM FOCUS Red and blue beads are in the ratio 3 : 7. There are 28 more blue beads than red beads. How many beads are there altogether? (3 marks) Decide what the number in the question stands for: the total, one person's share, or the difference. Each needs a different number of parts. |