Which is the greater ratio: 5 : 8 or 3 : 5?

Class 7Comparing QuantitiesComparing Quantities

A3 : 5
BThey are equal
C5 : 8
DThey cannot be compared

Step-by-Step Solution

Write both as fractions with the same denominator. LCM of 8 and 5 is 40, so

\frac{5}{8} = \frac{25}{40}

and

\frac{3}{5} = \frac{24}{40}

. Since 25 > 24, the ratio 5 : 8 is greater. (Cross-multiplying is the same check:

5 \times 5 = 25

against

8 \times 3 = 24

.) The trap is comparing only the second terms — 8 is bigger than 5, which tempts you to say 3 : 5 is the larger ratio.

Answer: C) 5 : 8

Key idea: Three forms of the same number

Fractions, decimals, and percentages are three notations for the same idea. Convert freely:

- **Fraction → percentage**: multiply by 100.

\frac{3}{5} = \frac{3}{5} \times 100% = 60%

.
- **Percentage → fraction**: divide by 100 and simplify.

75% = \frac{75}{100} = \frac{3}{4}

.
- **Decimal → percentage**: shift two places right. 0.34 = 34%.
- **Percentage → decimal**: shift two places left. 8% = 0.08.

With practice, this becomes automatic and you can move between forms without thinking.

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