Question

If $\frac{3}{4}+\frac{1}{6}$ must be represented as a sum of like fractions, it will be written as _______.

• A. $\frac{3}{12}$ + $\frac{1}{12}$
• B. $\frac{3}{6}$ + $\frac{1}{6}$
• C. $\frac{9}{12}$ + $\frac{2}{12}$
• D. $\frac{4}{8}$ + $\frac{6}{8}$

Answer 1

The correct option is C

$\frac{9}{12}$ + $\frac{2}{12}$

To represent $\frac{3}{4}+\frac{1}{6}$ using like fractions, we must convert both fractions to the same denominator.

The LCM of 4 and 6 is 12. So, we multiply both denominators accordingly to get a common denominator of 12.

We know that, 4 $\times$ 3 = 12 and 6 $\times$ 2 = 12, hence
$\frac{3}{4}$ = $\frac{3\times 3}{4\times 3}$ = $\frac{9}{12}$
$\frac{1}{6}$ = $\frac{1\times 2}{6\times 2}$ = $\frac{2}{12}$

$\therefore \frac{3}{4}+\frac{1}{6}$ can be written as $\frac{9}{12}+\frac{2}{12}.$