Question

How do you solve `\frac { 4} { 5} \div \frac { 1} { 2}`?

Answer 1

`8/5 = 1 3/5`

Explanation:

Write the problem as a complex fractions and then simplify by using the multiplicative inverse.

The fraction sign literally means to divide. So the problem is one fraction divided by a second fraction. The problem can be written

`(4/5)/(1/2)` This is called a complex fraction

To simplify the fraction multiply both sides by the inverse of the bottom fraction

`(1/2) xx (2/1) = (2/2) = (1/1)` By multiplying by the inverse the bottom term or fraction disappears.

The fairness principal states that what ever you do to one side must be done to the other side. ( The multiplication property of equality)

So both top fraction and the bottom fraction must be multiplied by the inverse `2/1` This gives

`{ ( 4/5) xx ( 2/1)} /{ (1/2) xx (2/1)}` The bottom fraction turns to `(1/1)`

Giving this

`{ (4 xx 2)/(5xx1)}/ (1/1) = 8/5`

`8/5 = 1 3/5`

The key to dividing fractions is to use the inverse of the second fraction which becomes the denominator of the complex fraction.

Answer 2

`8/5 = 1 3/5`

Explanation:

Dividing by any number is the same as multiplying by its reciprocal.

For example, saying "10 divided by 2", is the same as "half of 10"

In Maths:

`10 color(red)(div 2) = 10 color(red)(xx 1/2)`

Dividing by a fraction is exactly the same. Multiply by its reciprocal.

`4/5 color(red)(div 1/2)`
`color(white)(.x)darr`
`4/5 color(red)(xx 2/1)" "larr` no cancelling to be done. Multiply across

=`8/5`

=`1 3/5`