Question

Aunt Susanne baked a batch of cookies. She gave ${\frac{1}{5}}^{\text{th}}$ of the batch to Alice, ${\frac{6}{30}}^{\text{th}}$ of the batch to Ron, and ${\frac{3}{5}}^{\text{th}}$ of the batch to Max. Two among them get the same number of cookies. Who are they?

Answer 1

Fraction of cookies given to Alice
$=\frac{1}{5}$

Fraction of the cookies given to Ron
$=\frac{6}{30}$

Fraction of the cookies given to Max
$=\frac{3}{5}$

But $\frac{6}{30}=\frac{1\times 6}{5\times 6}=\frac{1}{5}$

(Cancelling the 6s)

Thus, $\frac{6}{30}$ and $\frac{1}{5}$ are equivalent fractions.

$\frac{3}{5}$ > $\frac{1}{5}$ as $3>1$

Hence, Alice and Ron get the same number of cookies. Also, not all of them get the same number of cookies.