# 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

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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