Question

(a) Amit used to be on the playground $4\frac{1}{2}$ times as much as his brother. Now he cut down $1\frac{1}{3}$ of the time he used to be on the playground as much as his brother. How much time does he spend on the playground when compared to his brother?

(b) The sum of two rational numbers is $\frac{-5}{8}$. If one of the numbers is $\frac{-6}{11}$, find the other number.

(c) Find x such that $\frac{-3}{8}$ and $\frac{x}{-24}$ are equivalent fractions.
[3 MARKS]

Answer 1

Each part: 1 Mark

(a) Amit played $4\frac{1}{2}=\frac{9}{2}$ times of his brother.

He cut down his play by $1\frac{1}{3}=\frac{4}{3}$
The duration Amit plays now
= $\frac{9}{2}-\frac{4}{3}=\frac{19}{6}=3\frac{1}{6}$.

So, now Amit plays $3\frac{1}{6}$ times as his brother.

(b) Let the number be x.

$\frac{-6}{11}+x=\frac{-5}{8}$

$x=\frac{-5}{8}-\frac{-6}{11}$

$x=\frac{-5}{8}+\frac{6}{11}$

$x=\frac{-7}{88}$

(c) For $\frac{-3}{8}$ and $\frac{x}{-24}$ to be equivalent.

$\Rightarrow \frac{-3}{8}=\frac{x}{-24}$

$\Rightarrow x=\frac{-3\times -24}{8}$

$\Rightarrow x=\frac{-3\times -3}{1}=9$