Ratios and Proportions Made Easy

Year 8 Mathematics Understanding relationships between quantities Building problem-solving skills

What is a Ratio?

A ratio compares two or more quantities Written as a:b or a/b or 'a to b' Shows the relationship between amounts Example: 3 red marbles to 5 blue marbles = 3:5

Ratio Hunt Activity

Look around the classroom Find 3 different ratios Record them in a:b format Share with a partner

Simplifying Ratios

Find the highest common factor (HCF) Divide both numbers by the HCF Example: 12:18 → HCF is 6 → 2:3 Always write in simplest form

Ratios vs Fractions

{"left":"Ratios compare parts to parts\nExample: 3 boys to 4 girls = 3:4","right":"Fractions compare parts to whole\nExample: 3 boys out of 7 total = 3/7"}

What are Proportions?

Two ratios that are equal Written as a:b = c:d or a/b = c/d Cross multiply to check: a×d = b×c Example: 2:3 = 4:6 because 2×6 = 3×4

Quick Check

Are these proportions correct? a) 3:4 = 6:8 b) 5:2 = 15:7 Use cross multiplication to verify!

Real-World Applications

Problem Solving Practice

Recipe scaling challenge If 2 cups flour makes 12 cookies How much flour for 18 cookies? Set up and solve the proportion

Practice Problems with Solutions

1) 4:7 = 12:? → Answer: 21 2) 3/5 = ?/20 → Answer: 12 3) 15:25 simplified → Answer: 3:5 4) 8:12 = 2:? → Answer: 3 5) If 5 pens cost $15, how much do 8 pens cost? → Answer: $24 6) 18:? = 6:4 → Answer: 12 7) 2:3:5 totals 40, find each part → Answer: 8, 12, 20 8) 7/9 = 21/? → Answer: 27 9) 16:20 in simplest form → Answer: 4:5 10) Scale 1:50000, 3cm represents ? → Answer: 1.5km