# How do you divide 1 1/ 2\div 3/ 4?

Apr 12, 2017

$2$

#### Explanation:

The value of 1 is the same as $\frac{2}{2}$

So write $1 \frac{1}{2}$ as $1 + \frac{1}{2} \text{ " ->" "2/2+1/2" "->" } \frac{3}{2}$

Giving: $\frac{3}{2} \div \frac{3}{4}$

$\textcolor{b l u e}{\text{Shortcut method}}$

$\text{ } \textcolor{g r e e n}{\frac{3}{2}} \div \textcolor{red}{\frac{3}{4}}$

$\text{ "color(red)(3/2)xxcolor(green)(4/3)" "->(cancel(3))/2xx4/(cancel(3))" cancelling out}$

This is the same process as

" "color(green)(3/(color(green)(3))xx4/(color(red)(2))

$\text{ } 1 \times \frac{4}{2} = 2$

Apr 14, 2017

Set up the problem as a fraction divided by a fraction. Resulting in the answer of $2$

#### Explanation:

The mixed number $1 \frac{1}{2}$ can be rewritten as an improper fraction.

$\frac{3}{2}$

Set up the problem as a complex fraction

$\frac{\frac{3}{2}}{\frac{3}{4}}$ The bar means to divide and also works as parentheses

Remove the bottom fraction by multiplying both the top and bottom fractions by the inverse of the bottom fraction.

$\frac{3}{4} \times \frac{4}{3} = 1$ multiplying by the inverse is math magic it makes the fraction disappear.

The multiplication property of equality is the fairness principle. what ever is done to one side must be also done to the other side. so

$\frac{\frac{3}{2} \times \frac{4}{3}}{\frac{3}{4} \times \frac{4}{3}} = \frac{3}{2} \times \frac{4}{3}$

$\frac{3}{2} \times \frac{4}{3} = \frac{12}{6}$

$\frac{12}{6} = 2$