Find the ratio of each of the following in simplest form:
$15 m m$ to $2 c m$

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Solution

Given ratio is $15 m m$ to $2 c m$
Convert the given ratio in same unit.
We know that,
$1 c m = 10 m m$
Therefore, $2 c m = 2 \times 10 m m = 20 m m$
$15 m m$ to $2 c m$ $=$ $15 m m$ to $20 m m$
Also, $15 m m : 20 m m = \frac{15 m m}{20 m m} = \frac{15}{20}$
Now simplest form of $\frac{15}{20}$ can be obtained by dividing both term by their HCF $5$
$\frac{15}{20} = \frac{\frac{15}{5}}{\frac{20}{5}} = \frac{3}{4}$
Hence, simplest form of $15 m m$ to $2 c m$ is $3 : 4$

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