Question

The ratio in its simplest form of $3m5cm$ to $2m75cm$ is:

• A. $\frac{35}{275}$
• B. $\frac{61}{55}$
• C. $\frac{61}{52}$
• D. $\frac{7}{55}$

Answer 1

The correct option is B

$\frac{61}{55}$

Find the simplest form

To find the simplest form of the ratio the units of numerator and denominator must be the same.

Conversion of unit in cm:

As we know., $1m=100cm$
$$\begin{gathered} 3m5cm=3\times 100+5cm \\ =305cm \end{gathered}$$

And

$$\begin{gathered} 2m75cm=2\times 100+75cm \\ =275cm \end{gathered}$$
The ratio is:
$\frac{305cm}{275cm}$ = $\frac{305}{275}$= $\frac{61\times 5}{55\times 5}$ = $\frac{61}{55}$
There is no common factor other than 1 in 61 and 55.
So, $\frac{61}{55}$ is the simplest form of the ratio $\frac{305}{275}$.

Hence, option (B) is correct.