Question

John spent $\frac{3}{4}$ hours doing homework. If $\frac{1}{4}$ hours of that time was spent doing math homework, what fraction of his total time spent doing homework did he spend on math?

Answer 1

Find the fraction:

The number of hours John spent doing homework is $\frac{3}{4}\mathrm{hours}$.

The number of hours John spent doing math homework is $\frac{1}{4}\mathrm{hours}$.

Divide the number of hours John spent doing math homework by the number of hours John spent doing homework to obtain the fraction $n$ of his total time spent doing homework did he spend on math.

$\begin{array}{rcl}n& =& \frac{{\displaystyle \frac{1}{4}}}{{\displaystyle \frac{3}{4}}}\\ & =& \frac{1}{4}\times \frac{4}{3}\\ & =& \frac{1}{3}\end{array}$

Hence, John spent $\frac{1}{3}$ of the total homework time doing the math homework.