Question

If John ate ${\frac{1}{3}}^{rd}$ of a cake and Anna ate ${\frac{1}{4}}^{th}$ of the cake, the portion of the cake they ate together is

• A. $\frac{2}{4}$
• B. $\frac{2}{3}$
• C. $\frac{7}{10}$
• D. $\frac{7}{12}$

Answer 1

The correct option is D $\frac{7}{12}$

Part of the cake that John ate = $\frac{1}{3}$
Part of the cake that Anna ate = $\frac{1}{4}$

So, part of the cake they ate together will be = $\frac{1}{3}+\frac{1}{4}$

Now, the fraction $\frac{1}{3}$ can be represented as:


So, John ate $\frac{4}{12}$ part of the cake.

Similarly, the fraction $\frac{1}{4}$ can be expressed as:


So, John ate $\frac{3}{12}$ part of the cake.

∴ The portion of the cake that John and Anna ate together will be $\frac{4}{12}+\frac{3}{12}$.

Calculating $\frac{4}{12}+\frac{3}{12}$, we get:


$\therefore$ The portion of the cake that John and Anna ate together is $\frac{7}{12}$ .