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Question

Express the ratio $45 : 108$ in its simplest form?

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Solution

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Factors of $45 = 3 \times 3 \times 5$

Factors of $108 = 2 \times 2 \times 3 \times 3 \times 3$

So, H.C.F of $45$ and $108$ is $3 \times 3 = 9$

$∴ 45 : 108 = \frac{45}{108} = \frac{45 \div 9}{108 \div 9} = \frac{5}{12} = 5 : 12$

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