6. Multiplication and Division of Fractions

Recall the following fraction facts:

When multiplying by a fraction, multiply numerators and multiply denominators:

`2/3xx 5/7=(2xx5)/(3xx7)=10/21`

If you can, simplify first :

`13/24xx 12/39=(1xx1)/(2xx3)=1/6`

(I canceled the `13` & `39` to give `1/3` and the `12` with the `24` to give `1/2`.)

When dividing by a fraction, invert and multiply:

`3/5-:2/7=3/5xx7/2=(3xx7)/(5xx2)=21/10=2 1/10`

(I multiplied by the inverse of `2/7`, which is `7/2`.)

When we do the same things with algebraic expressions, remember to SIMPLIFY FIRST, so that the problem is easy to perform.

Example 1

Simplify

`11/5xx13/33`

Answer:

Simplifying first, we cancel the 11 in the first fraction with the 33 on the bottom of the second fraction:

`11/5xx13/33=1/5xx13/3=13/15`

Example 2

Simplify:

`(18sy^3)/(ax^2)xx((ax)^2)/(3s)`

Example 3

Simplify:

`(sr^2)/(2t)-:(st)/(4)`

Exercises

Simplify:

(1) `5/16-:25/13`

(2) `(9x^2-16)/(x+1)-:(4-3x)`

(3) `(2x^2-18)/(x^3-25x)xx(3x-15)/(2x^2+6x)`

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