# How do you solve 20 1/2 div 3/4?

Oct 20, 2016

$27 \frac{1}{3}$

#### Explanation:

Convert the improper fraction to a improper fraction

$20 \frac{1}{2} = \frac{20 \cdot 2 + 1}{2} = \frac{41}{2}$

So the problem becomes

$\frac{41}{2} \div \frac{3}{4}$

Now you have to multiply by the reciprocal

$\frac{41}{2} \cdot \frac{4}{3}$

Cross cancel

$\frac{41}{\cancel{2}} \cdot \frac{2 \cancel{4}}{3}$

Multiply numerators and then denominators

$\frac{41}{1} \cdot \frac{2}{3} = \frac{82}{3}$

Convert to an improper fraction

$\frac{82}{3} = 27 \frac{1}{3}$

For another explanation please see the following tutorial.

Oct 20, 2016

$27.33 \mathmr{and} \frac{82}{3}$

#### Explanation:

When dividing fraction, you are actually multiplying by the reciprocal.

But first, it would be easier to work with improper fractions than with a mixed number.

So, to change $20 \frac{1}{2}$ into an improper fraction:

Multiply the denominator by the whole number

$2 \times 20 = 40$

Then add the numerator to the product of the denominator and whole number

$40 + 1 = 41$

Then put $41$ over the original denominator

$\frac{41}{2}$

Now, change the second fraction into its reciprocal

Which is just to switch the numerator and denominator

$\frac{3}{4} \implies \frac{4}{3}$

$\frac{41}{2} \times \frac{4}{3}$
$\frac{164}{6}$
$\frac{164}{6} = 27.33 \mathmr{and} \frac{82}{3}$