Question

Subtract $\frac{1}{2}$ from $\frac{6}{7},$ and choose the correct answer.

• A. $\frac{3}{14}$
• B. $\frac{5}{14}$
• C. $\frac{9}{14}$
• D. $\frac{2}{7}$

Answer 1

The correct option is B $\frac{5}{14}$

We have to subtract $\frac{1}{2}$ from $\frac{6}{7},$ so we have to find the value of $\frac{6}{7}-\frac{1}{2}$

As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 7 and 2

Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, ..

14 is the common multiple of 7 and 2. So, LCM of 7 and 2 is 14.

Step 2: Now, we have to convert the denominators of both the fractions into 14 (LCM of 7 and 2) without changing the fraction value.
$\frac{6}{7}=\frac{6\times 2}{7\times 2}=\frac{12}{14}$
and $\frac{1}{2}=\frac{1\times 7}{2\times 7}=\frac{7}{14}$

$\therefore \frac{6}{7}-\frac{1}{2}=\frac{12}{14}-\frac{7}{14}$
$=\frac{12-7}{14}$
$=\frac{5}{14}$