Question

How do you evaluate `\frac{11}{6}\div \frac{4}{3}`?

Answer 1

`11/8`

Explanation:

The division of two fractions can be expressed as:

`a/bdividec/d=a/btimesd/c`

Thus,

`11/6divide4/3=11/6times3/4=33/24`

Simplify: (both the numerator and denominator are divisible by `3`

`(33divide3)/(24divide3)=11/8`

Answer 2

Divide the top fraction by the bottom fraction resulting in `11/8` or `1 3/8`

Explanation:

Set up the two fractions as a single complex fraction.

`( 11/6)/(4/3)`

This complex fraction can be simplified by multiplying both the top and the bottom by the inverse of the bottom fraction `3/4`

`( 11/6 xx 3/4) / (4/3 xx 3/4)`

The bottom fraction becomes 1 and so math magic it disappears.
leaving

`11/6 xx 3/4`

The 3 can be factored out of the top and bottom leaving

`11/2 xx 1/4 = 11/8`

`11/8` is an improper fraction which can be changed to

`1 3/8`