# How do you simplify (5/6)/(1 1/4)?

Jan 8, 2017

$\frac{\frac{5}{6}}{1 \frac{1}{4}} = \frac{2}{3}$

#### Explanation:

Let us first convert mixed fraction $1 \frac{1}{4}$ into improper fraction

$1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}$

Now dividing by a fraction $\frac{a}{b}$ is equivalent to multiplying by its reciprocal $\frac{b}{a}$

Hence $\frac{\frac{5}{6}}{1 \frac{1}{4}}$

= $\frac{\frac{5}{6}}{\frac{5}{4}}$

= $\frac{5}{6} \times \frac{4}{5}$

= $\frac{\cancel{5}}{{\cancel{6}}^{3}} \times \frac{{\cancel{4}}^{2}}{\cancel{5}}$

= $\frac{2}{3}$

Jul 7, 2017

$\frac{2}{3}$

#### Explanation:

To divide and multiply, you need to work with common fractions, so change any mixed number into an improper fraction.

$1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4}$

There is a useful technique for dividing fractions given in this form:

$\frac{\textcolor{g r e e n}{\frac{a}{b}}}{\textcolor{m a \ge n t a}{\frac{c}{d}}} = \textcolor{g r e e n}{\frac{a}{b}} \div \textcolor{m a \ge n t a}{\frac{c}{d}} = \frac{a}{b} \textcolor{m a \ge n t a}{\times \frac{d}{c}} = \frac{a d}{b c}$

$\therefore \frac{\frac{\textcolor{red}{5}}{\textcolor{b l u e}{6}}}{\frac{\textcolor{b l u e}{5}}{\textcolor{red}{4}}} = \frac{\textcolor{red}{5 \times 4}}{\textcolor{b l u e}{6 \times 5}} \text{ } \leftarrow$ now simplify

$\frac{\cancel{5} \times {\cancel{4}}^{2}}{{\cancel{6}}^{3} \times \cancel{5}} = \frac{2}{3}$

Aug 17, 2017

Use the complex fraction theorem

#### Explanation:

$\frac{\frac{5}{6}}{1 \frac{1}{4}} = \frac{\frac{5}{6}}{\frac{5}{4}} \text{ } \leftarrow \left(1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\right)$

Using the multiplicative inverse and the multiplication property of equality multiply both the top fraction and the bottom fraction by the reciprocal of the bottom fraction $\frac{4}{5}$

$\frac{\frac{5}{6} \times \frac{4}{5}}{\frac{5}{4} \times \frac{4}{5}} \text{ "larr" " 5/4 xx 4/5 = 1" }$ leaving

$\frac{5}{6} \times \frac{4}{5}$

$= \frac{20}{30}$

$= \frac{2}{3}$