Three children shared a basket of mangoes in such a way that the first child took $\frac{1}{4}$ of the mangoes and the second $\frac{3}{4}$ of the remainder. What fraction of the mangoes did the third child take?

$\frac{3}{16}$

$\frac{7}{16}$

$\frac{9}{16}$

$\frac{13}{16}$

Correct answer is A

You can use any whole numbers (eg. 1. 2. 3) to represent all the mangoes in the basket.

If the first child takes $\frac{1}{4}$ it will remain 1 - $\frac{1}{4}$ = $\frac{3}{4}$

Next, the second child takes $\frac{3}{4}$ of the remainder

which is $\frac{3}{4}$ i.e. find $\frac{3}{4}$ of $\frac{3}{4}$

= $\frac{3}{4}$ x $\frac{3}{4}$

= $\frac{9}{16}$

the fraction remaining now = $\frac{3}{4}$ - $\frac{9}{16}$

= $\frac{12 - 9}{16}$

= $\frac{3}{16}$

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