State the following ratios are in proportion or not: $12 : 15 a n d 8 : 12$ .

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Solution

Step 1: Find the smallest form of the ratios
$12 : 15 = \frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5} = 4 : 5$
$8 : 12 = \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} = 2 : 3$
Step 2: Check the ratios are equal or not
Ratios $12 : 15 a n d 8 : 12$ are not equal.
Hence, $12 : 15 a n d 8 : 12$ are not in proportion.

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