# 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)

Didn't find what you are looking for on this page? Try search:

### Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Play a math game.

(Well, not really a math game, but each game was made using math...)

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

### Algebra Lessons on DVD

Easy to understand algebra lessons on DVD. See samples before you commit.