Express the following ratio in the simplest form: $3 y e a r s : 9 m o n t h s$ .

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Solution

Step 1: Convert years to months
$3 y e a r s = 3 \times 12 m o n t h s = 36 m o n t h s$ $(1 y e a r = 12 m o n t h s)$
Step 2: Convert ratio into fraction
$36 m o n t h s : 9 m o n t h s = \frac{36}{9}$
Step 3: Divide numerator and denominator by 9
Highest Common Factor Of two terms are $9$ .
$\frac{36 \div 9}{9 \div 9} = \frac{4}{1} = 4 : 1$
Hence, the simplest form of $3 y e a r s : 9 m o n t h s$ is $4 : 1$ .

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