Write the ratio of the quantities in the simplest form
$2 m 200 c m$ $t o$ $4 m 400 c m$

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Solution

Step-1: Convert $2 m 200 c m$ into $m$
$2 m 200 c m$ $=$ $2 m + \frac{200}{100} m =$ $2 m + 2 m =$ $4 m$ ( As $100 c m = 1 m$ )
Step-2: Convert $4 m 400 c m$ into $m$
$4 m 400 c m$ $=$ $4 m + \frac{400}{100} m =$ $4 m + 4 m =$ $8 m$ ( As $100 c m = 1 m$ )
Step-3: Write $4 m$ to $8 m$ in the form of a ratio
$4 m$ to $8 m$ $=$ $4 : 8$
Step-4: Simplify the ratio $4 : 8$
$4 : 8$ $=$ $\frac{4 \div 4}{8 \div 4}$ ( To simplify $4 : 8$ divide it by HCF of $4$ and $8$ The HCF of $4$ and $8$ is $4$ )
$4 : 8$ $=$ $\frac{1}{2}$ $=$ $1 : 2$
Hence, the ratio of quantities $2 m 200 c m$ $t o$ $4 m 400 c m$ is $1 : 2$

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