Question

By what number should $3\frac{1}{4}$ be multiplied to get $2\frac{1}{6}$?

• A. $\frac{24}{169}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{2}{3}$

$3\frac{1}{4}\times (?)=2\frac{1}{6}$

We need to find the unknown number here.
To find the unknown number we need to divide $2\frac{1}{6}$ by $3\frac{1}{4}$

To find: $2\frac{1}{6}÷3\frac{1}{4}$

First we need to convert the mixed fractions to improper fractions
$\Rightarrow 2\frac{1}{6}÷3\frac{1}{4}=\frac{2\times 6+1}{6}÷\frac{3\times 4+1}{4}$

$\Rightarrow 2\frac{1}{6}÷3\frac{1}{4}=\frac{13}{6}÷\frac{13}{4}$

Flip the second fraction and then multiply the flipped second fraction by first fraction.

$\Rightarrow 2\frac{1}{6}÷3\frac{1}{4}=\frac{13}{6}\times \frac{4}{13}=\frac{4}{6}=\frac{2}{3}$

$\therefore 2\frac{1}{6}÷3\frac{1}{4}=\frac{2}{3}$