# How do you simplify 5 1/2 div 3?

Mar 10, 2018

$\frac{11}{6}$

#### Explanation:

We can rewrite the mixed number as an improper fraction by multiplying the denominator by the whole number, and adding it to the numerator.

The denominator will stay the same and we get:

$\left(\frac{11}{2}\right) \div \left(\frac{3}{1}\right)$

As our new expression. When we divide fractions, we multiply the second by the reciprocal. Doing this, we get:

$\frac{11}{2} \cdot \frac{1}{3}$

When we multiply fractions, we just multiply straight across to get:

$\frac{11}{6}$

As our final answer. Hope this helps!

Mar 10, 2018

See a solution process below:

#### Explanation:

First, convert the mixed number to an improper fraction:

$5 \frac{1}{2} = 5 + \frac{1}{2} = \left(\frac{2}{2} \times 5\right) + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{10 + 1}{2} = \frac{11}{2}$

Next, we can rewrite the expression as:

$\frac{11}{2} \div \frac{3}{1} \implies \frac{\frac{11}{2}}{\frac{3}{1}}$

We can evaluate the expression using this rule for dividing fractions:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{11}}{\textcolor{b l u e}{2}}}{\frac{\textcolor{g r e e n}{3}}{\textcolor{p u r p \le}{1}}} \implies \frac{\textcolor{red}{11} \times \textcolor{p u r p \le}{1}}{\textcolor{b l u e}{2} \times \textcolor{g r e e n}{3}} \implies \frac{11}{6}$

If necessary, we can convert this to a mixed number as:

$\frac{11}{6} = \frac{6 + 5}{6} = \frac{6}{6} + \frac{5}{6} = 1 + \frac{5}{6} = 1 \frac{5}{6}$