Ever wondered why a recipe that serves 2 can be easily changed to serve 8? That's ratio and proportion working behind the scenes.
💡 In Simple Words: A ratio compares two amounts, like 2 apples to 3 oranges. A proportion says two ratios are equal, like 2:3 = 4:6. When you see a word problem, you just match the pieces and solve.
What is a Ratio?
A ratio is a way to show how much of one thing there is compared to another. Think of it as a recipe: if you need 2 cups of flour for every 1 cup of sugar, the ratio of flour to sugar is 2:1.
Understanding Proportion
A proportion tells you that two ratios are the same. Imagine two identical maps. If 1 cm on the first map equals 5 km in real life, and 2 cm on the second map also equals 10 km, the two ratios 1:5 and 2:10 are proportionate.
Steps to Solve Ratio Word Problems
- Read the problem carefully – pick out the numbers and what they are compared to.
- Write the given ratio using the colon (: ) or fraction form.
- Set up a proportion – place the unknown side in the same position as the known side.
- Cross‑multiply (multiply opposite corners) and solve for the unknown.
- Check your answer – does it make sense in the story?
Worked Example 1: Mixing Paint
A painter mixes red and white paint in the ratio 3:2. If he wants 25 litres of the final colour, how many litres of each colour does he need?
Step 1: Total parts = 3 + 2 = 5.
Step 2: Each part = 25 ÷ 5 = 5 litres.
Step 3: Red = 3 × 5 = 15 litres, White = 2 × 5 = 10 litres.
So the painter uses 15 L red and 10 L white.
Worked Example 2: Map Distance
A map shows that 4 cm represent 12 km. How many kilometres does 9 cm represent?
Write the proportion: 4 cm / 12 km = 9 cm / x km.
Cross‑multiply: 4 × x = 9 × 12 → 4x = 108 → x = 27 km.
The 9 cm on the map equals 27 km in real life.
Quick Comparison: Ratio vs Proportion
| Aspect | Ratio | Proportion |
|---|---|---|
| What it shows | Comparison of two quantities | Equality of two ratios |
| Typical form | 3:5 or 3/5 | 3:5 = 6:10 |
| Use in word problems | Identify the parts | Link known and unknown parts |
📝 Likely Exam Questions
- Question: The ratio of boys to girls in a class is 4:5. If there are 36 students, how many boys are there?
Answer: Total parts = 4 + 5 = 9. Each part = 36 ÷ 9 = 4. Boys = 4 × 4 = 16. - Question: A recipe requires milk and cocoa in the ratio 7:3. How much cocoa is needed if you use 21 cups of milk?
Answer: Set proportion 7/3 = 21/x → 7x = 63 → x = 9 cups cocoa. - Question: On a map, 5 cm represent 20 km. How many kilometres does 13 cm represent?
Answer: 5/20 = 13/x → 5x = 260 → x = 52 km. - Question: A chemist mixes acid and water in the ratio 1:4. To make 25 L of solution, how much acid is required?
Answer: Total parts = 1 + 4 = 5. Each part = 25 ÷ 5 = 5 L. Acid = 1 × 5 = 5 L.