Question

Add $\frac{5}{21}$ with $\frac{3}{28}$ by taking LCM of the denominators.

• A. $\frac{29}{84}$
• B. Those numbers cannot be added.
• C. $\frac{31}{84}$

Answer 1

The correct option is A $\frac{29}{84}$

To add $\frac{5}{21}$ with $\frac{3}{28}$ we need to make the denominators same.

To reduce calculation, we convert the denominators to their LCM.
Using ladder diagram,
LCM $=7\times 3\times 2\times 2=84$

$\therefore$ We convert the denominators to $84.$

$\frac{5}{21}=\frac{5}{21}\times \frac{4}{4}=\frac{5\times 4}{21\times 4}=\frac{20}{84}$
Similarly,
$\frac{3}{28}=\frac{3}{28}\times \frac{3}{3}=\frac{3\times 3}{28\times 3}=\frac{9}{84}$

Now, as the denomiators are same, the numerators can be added.
$\frac{5}{21}+\frac{3}{28}=\frac{20}{84}+\frac{9}{84}=\frac{20+9}{84}=\frac{29}{84}$