Question

Jack and Joseph ate $\frac{3}{4}$ and $\frac{2}{3}$ of a cake respectively. Who ate less?

• A. Jack
• B. Joseph
• C. Both ate equally
• D. None of the above

Answer 1

The correct option is B Joseph

Let's compare $\frac{3}{4}\text{and}\frac{2}{3}:$

Step 1: Find the LCM of denominators of the given fractions.
i.e. LCM of 4 and 3
4 can be written as $2:2\times 2$
3 can be written as $3:3\times 1$

Taking the factors with highest powers common, we get
$2^2$ from 4 and $3^1$ from 3.

Multiplying them, we get $2^2\times 3=12$ as the required LCM.

Step 2: Now, we multiply $\frac{3}{4}$ and $\frac{2}{3}$ with $3$ and $4$ respectively to make their denominators as $12.$

$\therefore \frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$

and $\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$

Step 3: When fractions have the same denominator, then the smallest fraction is the one with the smallest numerator.

So, just compare the numerators 9 and 8.

Since $8<9$
$\therefore \frac{8}{12}<\frac{9}{12}$
$\Rightarrow \frac{2}{3}<\frac{3}{4}$

So, Joseph ate less cake than Jack.