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Class 8 Proportional Reasoning-1: cheat sheet
CBSE Mathematics. Ratios compare quantities of the same kind. Share an amount in a ratio, test for proportion, and use the unitary method to find the better buy.
Key ideas
- A ratio compares two quantities in the same unit; simplify it by dividing both parts by their HCF.
- Convert to the same unit first: 50 cm : 2 m = 50 : 200 = 1 : 4.
- To share in the ratio a : b, divide the total into a + b equal parts.
- Four numbers are in proportion when the first two have the same ratio as the last two.
- Unitary method: find the value of one unit, then multiply.
- The better buy is the one with the lower price per unit.
Remember
| Sharing in a : b | first share = total × a ÷ (a + b) |
| Proportion | a : b = c : d ⇔ a × d = b × c |
| Unit price | price ÷ number of units |
Watch out
- Comparing quantities in different units.
- Dividing the total by a and b instead of by a + b.
- Choosing the cheaper pack instead of the cheaper price per unit.
Worked example
Pack A has 3 soaps for Rs 78. Pack B has 5 soaps for Rs 140. Which is the better buy?
Working: A: 78 ÷ 3 = 26; B: 140 ÷ 5 = 28
Answer: Pack A (Rs 26 per soap)
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