Question

By what number should $5\frac{1}{3}$ be multiplied to get $4\frac{1}{2}$?

• A. $\frac{32}{27}$
• B. $\frac{27}{32}$
• C. $\frac{1}{24}$

Answer 1

The correct option is B $\frac{27}{32}$

$5\frac{1}{3}\times (?)=4\frac{1}{2}$

We need to find the unknown number here.
To find the unknown number we need to divide $4\frac{1}{2}$ by $5\frac{1}{3}$

To find: $4\frac{1}{2}÷5\frac{1}{3}$

First we need to convert the mixed fractions to improper fractions
$\Rightarrow 4\frac{1}{2}÷5\frac{1}{3}=\frac{4\times 2+1}{2}÷\frac{5\times 3+1}{3}$

$\Rightarrow 4\frac{1}{2}÷5\frac{1}{3}=\frac{9}{2}÷\frac{16}{3}$

Take a reciprocal of the second fraction and multiply that reciprocal by the first fraction as follows.

$\therefore 4\frac{1}{2}÷5\frac{1}{3}=\frac{9}{2}÷\frac{16}{3}=\frac{9}{2}\times \frac{3}{16}=\frac{9\times 3}{2\times 16}=\frac{27}{32}$

$\therefore 4\frac{1}{2}÷5\frac{1}{3}=\frac{27}{32}$