# Question #9bc49

Jan 29, 2018

$\frac{7}{6}$

#### Explanation:

We have: $\frac{\frac{7}{8}}{\frac{3}{4}}$

When dividing fractions we must apply the following rule:

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \cdot \frac{d}{c}$

So $\frac{\frac{7}{8}}{\frac{3}{4}} \to \frac{7}{8} \cdot \frac{4}{3} = \frac{28}{24}$

We can simplify $\frac{28}{24}$ since both numbers are divisible by $4$

$\frac{28 \div i \mathrm{de} 4}{24 \div i \mathrm{de} 4} = \frac{7}{6}$

Jan 29, 2018

$\frac{28}{24} = \frac{7}{6} = 1 \frac{1}{6}$

#### Explanation:

The answer can be expressed as a fraction a "reduced" fraction or a mixed number .

A fraction is actually a division problem so a fraction divided by a fraction is a complex fraction. Write the first fraction as the numerator and the second as the denominator of the complex fraction.

$\frac{\frac{7}{8}}{\frac{3}{4}}$

Now to simply the complex fraction multiple both the numerator and the denominator by the inverse of the bottom (second) fraction. Multiplying by the inverse equals 1 removing the bottom fraction.

$\frac{\frac{7}{8} \times \frac{4}{3}}{\frac{3}{4} \times \frac{4}{3}}$

This is the same as multiplying by 1 which does not change the value of the fraction. This gives

$\frac{7}{8} \times \frac{4}{3}$ : $\frac{3}{4} \times \frac{4}{3} = 1$

$\frac{7}{8} \times \frac{4}{3} = \frac{28}{24}$

$\frac{\frac{28}{4}}{\frac{24}{4}} = \frac{7}{6}$

$\frac{7}{6} = 1 \frac{1}{6}$