The big picture
The juice seller keeps one ratio the same. Here are all ten ideas, in order.
| Idea | Remember | Example |
|---|---|---|
| Two questions | Subtract for more. Divide for times. | 18, 12 → 6 m, 1.5 times |
| What it says | Boys : girls names two groups. Girls : class names a group and the whole. | 18 : 12 = 3 : 2 |
| Bigger numbers | Multiply both parts by the same number (not 0). Adding the same number to both usually changes it. | 3 : 2 × 4 = 12 : 8 |
| Simplest form | Match units. Cut by the highest factor | 500 g : 2 kg = 1 : 4 |
| Sharing | Count the parts. Find one. Hand out. | ₹350 in 3 : 4 = ₹150, ₹200 |
| Two that match | Multiply across. Outer equals inner. | 3 : 4 and 9 : 12, both 36 |
| Value of one | If each is worth the same: divide, multiply, divide back. | 5 → ₹90, so 8 → ₹144 |
| Growing together | The same division in every row | rice 40; taxi 62, 37 |
| Rates | Keep the units. Runs an over is runs ÷ overs. | 48 ÷ 8 = 6 runs an over |
| Scales | Paper length × scale = real length | 4 cm × 50,000 = 200,000 cm = 2 km |
Chapter 7 of Part I is Proportional Reasoning-1. Open it and see what it does with these ideas.
Next: Fractions in Disguise. It uses the same habit. This time the second part is fixed at a hundred.