Why Ratio and Proportion Matter in Real Life?
Ever wondered how a recipe keeps its taste when you double it? That's ratio and proportion at work. In exams, the same idea pops up as word problems.
💡 In Simple Words: A ratio tells you how many parts of one thing compare to another. A proportion says two ratios are equal. Solve them by finding the missing part that keeps the balance.
What Exactly Is a Ratio?
A ratio is just a way to compare two quantities. Think of it like a score in a game: 3 : 2 means for every 3 of the first item, there are 2 of the second.
Understanding Proportion
A proportion is an equation that says two ratios are the same. For example, 3 : 4 = 6 : 8. Both sides simplify to the same fraction (3/4).
How to Solve Ratio Word Problems
Most problems follow a simple pattern. Follow these steps and you’ll feel confident.
Step‑by‑step guide
- Read the problem carefully. Highlight numbers and what they represent.
- Identify the given ratio. Ask yourself, "What is being compared?" li> Write the proportion. Put the known parts on one side and the unknown part on the other.
- Cross‑multiply. Multiply the top left number by the bottom right, and the bottom left by the top right.
- Solve for the unknown. Keep the equation simple, then divide.
- Check the answer. Plug it back into the original story to see if it makes sense.
Worked Example (ICSE Style)
Problem: A school has a boys‑to‑girls ratio of 5 : 3. If there are 200 students in total, how many girls are there?
Step 1 – Read: Boys : Girls = 5 : 3, total = 200.
Step 2 – Identify ratio: 5 parts boys, 3 parts girls. Total parts = 5 + 3 = 8.
Step 3 – Write proportion: (Number of girls) / 200 = 3 / 8.
Step 4 – Cross‑multiply: Number of girls × 8 = 3 × 200 → 8 × girls = 600.
Step 5 – Solve: girls = 600 / 8 = 75.
Step 6 – Check: Girls = 75, Boys = 200 - 75 = 125. Ratio 125 : 75 simplifies to 5 : 3. All good!
Another Example with Proportion
Problem: A map uses a scale of 1 cm : 5 km. If the distance between two towns on the map is 7 cm, what is the real distance?
Write the proportion: 1 cm / 5 km = 7 cm / x km.
Cross‑multiply: 1 × x = 5 × 7 → x = 35 km. So the towns are 35 km apart.
Quick Reference Table
| Step | What to Do | Why It Helps |
|---|---|---|
| 1 | Read & highlight | Stops you from missing numbers |
| 2 | Find the ratio | Shows the relationship |
| 3 | Set up proportion | Turns words into an equation |
| 4 | Cross‑multiply | Gets rid of fractions |
| 5 | Solve & check | Ensures the answer fits the story |
Common Mistakes to Avoid
- Mixing up which quantity goes on which side of the proportion.
- Forgetting to add all parts of the ratio before using the total.
- Skipping the final check – a quick plug‑in catches most errors.
📝 Likely Exam Questions
- Question: The ratio of red to blue marbles in a bag is 4 : 5. If there are 72 marbles in total, how many red marbles are there?
Answer: Total parts = 4 + 5 = 9. One part = 72 ÷ 9 = 8. Red marbles = 4 × 8 = 32. - Question: A recipe calls for sugar and flour in the ratio 2 : 3. If you use 500 g of flour, how much sugar do you need?
Answer: Set up 2 / 3 = sugar / 500. Cross‑multiply: 2 × 500 = 3 × sugar → sugar = 1000 ÷ 3 ≈ 333 g. - Question: A car travels 150 km in 3 hours. Using the same speed, how far will it travel in 7 hours?
Answer: Speed ratio = distance / time = 150 / 3 = 50 km per hour. Proportion: 150 km / 3 h = x km / 7 h → x = 50 × 7 = 350 km. - Question: In a class, the boys‑to‑girls ratio is 7 : 5. If there are 84 students, how many boys are there?
Answer: Total parts = 12. One part = 84 ÷ 12 = 7. Boys = 7 × 7 = 49.