Question

Choose the correct value for the following expression
$\frac{55}{4}÷\frac{10}{2}=$

• A. $4\frac{2}{3}$
• B. $3\frac{2}{4}$
• C. $2\frac{3}{4}$
• D. $1\frac{3}{4}$

Answer 1

The correct option is C $2\frac{3}{4}$

Take a reciprocal of the second fraction and multiply that reciprocal by the first fraction as follows
$\frac{55}{4}÷\frac{10}{2}=\frac{55}{4}\times \frac{2}{10}=\frac{55\times 2}{4\times 10}$

Now, we need to simplify the resulting fraction
$\frac{55\times 2}{4\times 10}=\frac{5\times 11\times 2}{2\times 2\times 2\times 5}$

Cancel out the common factors of numerator and denominator of the fraction
$\frac{5\times 11\times 2}{2\times 2\times 2\times 5}=\frac{11}{2\times 2}=\frac{11}{4}$

$\therefore \frac{55}{4}÷\frac{10}{2}=\frac{11}{4}$

$\Rightarrow \frac{11}{4}=\frac{4\times 2+3}{4}=2+\frac{3}{4}=2\frac{3}{4}$

Hence, $\frac{55}{4}÷\frac{10}{2}=2\frac{3}{4}$