Question

How do you simplify `(4/5)/(6 2/3)`?

Answer 1

When you see a mixed number, get rid of it!

Explanation:

`6 2/3 = 20/3`.

Therefore, your complex fraction is equivalent to

`(4/5) / (20/3)`.

Now you are simply dividing two ordinary fractions. "Invert and multiply."

Answer 2

`3/25`

Explanation:

To simplify `4/5-:6 2/3` follow the steps shown, changing any

`color(blue)" mixed numbers to improper fractions"`

`rArr6 2/3=20/3`

`• " leave the first fraction"`

`• " change division to multiplication"`

`• " invert (turn upside down) the second fraction"`

`• " cancel, if possible, and simplify"`

`rArr4/5xx3/20larrcolor(red)" multiply and invert"`

`=cancel(4)^1/5xx3/cancel(20)^5larrcolor(red)" cancelling by 4"`

Multiply remaining values on numerator/denominator.

`=(1xx3)/(5xx5)`

`=3/25`

Answer 3

`3/25`

Explanation:

The complex fraction `(4/5)/(6 2/3)` can also be written as:

`(4/5) div(6 2/3)" "` change to improper fractions

`= 4/5 div 20/3" "larr` multiply by the reciprocal

`=cancel4/5 xx3/cancel20^5`

`=3/25`