# What’s nine tenths divided by two fifths?

Nov 20, 2017

2 1/4 or 9/4

#### Explanation:

Set up the problem as a complex fraction( one fraction divided by a second fraction)

$\frac{\frac{9}{10}}{\frac{2}{5}}$

To simplify the complex fraction multiply both the top and the bottom fractions by the inverse of the bottom fraction. ( multiplication property of equality )

$\frac{\frac{9}{10} \times \frac{5}{2}}{\frac{2}{5} \times \frac{5}{2}}$

The bottom fraction disappears

$\frac{2}{5} \times \frac{5}{2} = 1$ This leaves

$\frac{9}{10} \times \frac{5}{2}$ This gives

$\frac{45}{20}$ dividing both sides by 5 gives

$\frac{9}{4}$ which is an improper fraction. As a mixed number is

$2 \frac{1}{4}$

Nov 24, 2017

$\frac{9}{4}$

#### Explanation:

$\frac{9}{10} : \frac{2}{5}$

There is a simple rule that says:

$a : \left(\frac{b}{c}\right) = a \times \frac{c}{b}$

So, we can apply it:

$\frac{9}{10} : \frac{2}{5} = \frac{9}{10} \times \frac{5}{2} = \frac{9}{2 \cdot \cancel{5}} \times \frac{\cancel{5}}{2} = \frac{9}{4}$

Nov 24, 2017

See a solution process below:

#### Explanation:

We can write this expression as:

$\frac{9}{10} \div \frac{2}{5} \implies \frac{\frac{9}{10}}{\frac{2}{5}}$

We can now use this rule for dividing fractions to evaluate the expression:

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

$\frac{\frac{\textcolor{red}{9}}{\textcolor{b l u e}{10}}}{\frac{\textcolor{g r e e n}{2}}{\textcolor{p u r p \le}{5}}} \implies \frac{\textcolor{red}{9} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{10} \times \textcolor{g r e e n}{2}} \implies \frac{\textcolor{red}{9} \times \textcolor{b l u e}{\cancel{\textcolor{p u r p \le}{5}}}}{\textcolor{p u r p \le}{\cancel{\textcolor{b l u e}{10}}} 2 \times \textcolor{g r e e n}{2}} \implies \frac{9}{4}$

If necessary, we can convert this into mixed number:

$\frac{9}{4} \implies \frac{8 + 1}{4} = \frac{8}{4} + \frac{1}{4} = 2 + \frac{1}{4} = 2 \frac{1}{4}$