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

Mar 15, 2018

See a solution process below:

#### Explanation:

First, convert each mixed number to an improper fraction:

$2 \frac{1}{2} = 2 + \frac{1}{2} = \left(\frac{2}{2} \times 2\right) + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$

$3 \frac{1}{5} = 3 + \frac{1}{5} = \left(\frac{5}{5} \times 3\right) + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{15 + 1}{5} = \frac{16}{5}$

We can now rewrite the expression as:

$\frac{5}{2} \div \frac{16}{5} \implies \frac{\frac{5}{2}}{\frac{16}{5}}$

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

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

$\frac{\frac{\textcolor{red}{5}}{\textcolor{b l u e}{2}}}{\frac{\textcolor{g r e e n}{16}}{\textcolor{p u r p \le}{5}}} \implies \frac{\textcolor{red}{5} \times \textcolor{p u r p \le}{5}}{\textcolor{b l u e}{2} \times \textcolor{g r e e n}{16}} = \frac{25}{32}$

Mar 15, 2018

Flip the dividing fraction and multiply the two together! You'll get $\frac{25}{32}$

#### Explanation:

The first thing to do is make these mixed fractions into their improper forms:

$2 \frac{1}{2} \div 3 \frac{1}{5} = \frac{5}{2} \div \frac{16}{5}$

Now, we'll invert the divisor:

${\left(\frac{16}{5}\right)}^{- 1} = \frac{5}{16}$

and multiply the first fraction by the inverse of the second:

$\frac{5}{2} \cdot \frac{5}{16} = \textcolor{red}{\frac{25}{32}}$

Mar 15, 2018

$\frac{25}{32}$

#### Explanation:

First let's write these as Improper Fractions ("top heavy fractions")

$\textcolor{\mathmr{and} a n \ge}{2} + \frac{\textcolor{g r e e n}{1}}{\textcolor{b l u e}{2}}$ is the same as $\left(\textcolor{\mathmr{and} a n \ge}{2} \times \textcolor{b l u e}{2}\right) + \textcolor{g r e e n}{1}$ over the denominator $\textcolor{b l u e}{2}$ or $\frac{5}{2}$

$\textcolor{\mathmr{and} a n \ge}{3} + \frac{\textcolor{g r e e n}{1}}{\textcolor{b l u e}{5}}$ is the same as $\left(\textcolor{\mathmr{and} a n \ge}{3} \times \textcolor{b l u e}{5}\right) + \textcolor{g r e e n}{1}$ over the denominator $\textcolor{b l u e}{5}$ or $\frac{16}{5}$

So now we have $\frac{5}{2} \div \frac{16}{5}$

When we divide fractions, we multiply by the recipricol ($\frac{1}{t h e \textcolor{w h i t e}{0} f r a c t i o n}$)

$\frac{5}{2} \times \frac{5}{16}$

Now we multiply straight across and get $\frac{25}{32}$