Question

Identify the expression which results in a terminating decimal number.

• A. $\frac{1}{2}÷\frac{2}{7}+\frac{6}{7}$
• B. $\frac{5}{14}+\frac{1}{2}÷\frac{7}{2}$

Answer 1

The correct option is B $\frac{5}{14}+\frac{1}{2}÷\frac{7}{2}$

Let's evaluate each expression one by one by following the PEMDAS rule.

$\to \frac{1}{2}÷\frac{2}{7}+\frac{6}{7}$
$=\frac{1}{2}\times \frac{7}{2}+\frac{6}{7}$
$=\frac{7}{4}+\frac{6}{7}$
$=\frac{7\times 7+6\times 4}{4\times 7}$
Without solving further, we can observe that the denominator is a multiple of $7$
we know that for a fraction to be terminating decimal its denominator should be multiple of $2$ or $5.$

Hence, the first expression will result in a non-terminating decimal number.

Let's check for option(b)
$\to \frac{5}{14}+\frac{1}{2}÷\frac{7}{2}$
$=\frac{5}{14}+\frac{1}{2}\times \frac{2}{7}$
$=\frac{5}{14}+\frac{1}{7}$
$=\frac{5+2\times 1}{14}$
$=\frac{7}{14}$
$=\frac{1}{2}$
The factors of the denominator are $2$ and $1.$
Hence, it will result in a terminating decimal number.