# How do you simplify 4/5 div 1/4?

##### 2 Answers
Aug 3, 2016

$\frac{16}{5}$

#### Explanation:

Dividing with fractions is not very different from multiplication.

STEP 1. Change any mixed numbers to improper fractions.

STEP 2: Dividing by a fraction is the same as multiplying by its reciprocal.

Change the division sign into multiplication and flip the fractions which follow.

STEP 3. Simplify by cancelling common factors in the numerator an denominator. (Only cancel through a X sign!)

STEP 4. Multiply: $\text{(top x top)"/("(bottom x bottom)}$

Check for final simplifying, but if you have cancelled completely in step 3, there should be no simplifying necessary.

$\frac{4}{5} \textcolor{red}{\div \frac{1}{4}} \text{ becomes}$

$\frac{4}{5} \textcolor{red}{\times \frac{4}{1}}$

=$\frac{16}{5}$

Aug 5, 2016

$\frac{16}{5}$
This problem can be written as $\frac{\frac{4}{5}}{\frac{1}{4}}$
multiply both parts by $\frac{4}{1}$

#### Explanation:

$\frac{\frac{4}{5}}{\frac{1}{4}}$
is a complex fraction. It is best to simplify complex things.

The denominator, or bottom part of this complex fraction is $\frac{1}{4}$

to make $\frac{1}{4}$ disappear, multiply by $\frac{4}{1}$, its inverse

$\frac{1}{4}$ x $\frac{4}{1}$ = 1 abbra cabra math magic its gone

However to be fair whatever is done to the bottom must be done to the top, the numerator $\frac{4}{5}$

$\frac{4}{5} \times \frac{4}{1} = \frac{4 \times 4}{5 \times 1} = \frac{16}{5}$

Remember write the division of two fractions as a complex or one complex fraction. Make the bottom fraction disappear using math magic ( reciprocal or inverse) But be fair do the same thing to the top fraction as you do to the bottom fraction. Easy to remember and you will never get confused as to which fraction to invert.