Find the ratio of $1 m 20 c m : 3 m 20 c m$ in the simplest form.

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Solution

Step 1: Converting the numbers into the same unit
To find the ratio of two quantities their units must be the same.
We know that $1 m = 100 c m$
$1 m 20 c m$ $= (1 \times 100) + 20 c m$
$= 100 c m + 20 c m$
$= 120 c m$
$3 m 20 c m$ $= (3 \times 100) + 20 c m$
$= 300 c m + 20 c m$
$= 320 c m$

Step 2: Finding the ratio
$1 m 20 c m : 3 m 20 c m$
$=$ $\frac{1 m 20 c m}{3 m 20 c m}$
$= \frac{120 c m}{320 c m}$
$= \frac{12}{32} = \frac{4 \times 3}{4 \times 8} = \frac{3}{8}$
Here, $3$ and $8$ have no common factor other than $1$ .
Thus, $\frac{3}{8}$ is the simplest form of fraction $\frac{120}{320}$
Hence, the simplest ratio is $3 : 8$ .

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