Question

A rectangle is divided into certain number of equal parts. If 16 of the parts, so formed represent the fraction $\frac{1}{4}$, find the number of parts in which the rectangle has been divided.

• A. 32
• B. 64
• C. 96
• D. 128

Answer 1

The correct option is B 64

Let a rectangle be divided into $x$ equal parts.
Now, 16 of the parts represent = $\frac{1}{4}$
Also, 16 parts of $x$ = $\frac{16}{x}$
$\therefore$ $\frac{1}{4}$ = $\frac{16}{x}$
$\frac{16}{x}$ is an equivalent fraction of $\frac{1}{4}$.
The numerator 16 of the equivalent fraction has been obtained by multiplying 16 by 1, so the denominator of the equivalent fraction will be 4 multiplied by 16 too.
$\Rightarrow$ $\frac{1\times 16}{4\times 16}$ = $\frac{16}{x}$
$\Rightarrow$ $\frac{16}{64}$ = $\frac{16}{x}$
So, $x$ = 64 parts
Hence, the rectangle is divided into 64 equal parts.