Download Dividing Monomials

Name: ________________
Dividing Monomials
Linking Dividing Monomials to Basic Arithmetic

Working with division in Arithmetic is a lot like division of monomials in Algebra. In arithmetic, you
use your knowledge of factors to help you. Look at this example of division using factors. When
you review the strategy you use in Arithmetic, algebra will make more sense. Simply show the
factors, cancel out the factors (which is division) and you will be left with your solution.
Example:
Dividing Monomials - Basic Algebra

Here's a basic monomial. Notice that when you divide the monomial, you're dividing the numerical
coefficients (the 24 and the 8) and you're dividing the literal coefficients (a and b).
Example:
Division of a Monomial Involving Exponents - Basic Algebra

Once again you divide the numerical (the numbers) and the variable. However, you divide the
like variable factors (what the numerator and the denominator have in common) by subtracting
their exponents (5-2).
Example:
20a
(5  4)  a  a  a  a  a

 4  a  a  a  4a 3
2
5a
5 a  a
5
Division of Monomials - Another Example

Divide the numbers and variables, dividing the like variable factors by subtracting the exponents.
-
Quotients of
Powers
You can divide powers with the same base by
subtracting exponents for all integers m and n and
any nonzero number, a.
Ex:
Zero
Exponent
Negative
Exponents
am
 a mn
n
a
For any nonzero number a
Ex: a  1
For any nonzero number a and any integer n,
0
am 
1
am
and
1
 am
am
Practice Problems:
1.
a 2b9
a 2b8
9ab4c
4.
6a 5b2
2.
g 7 h2
g 5 h0
 9ab 4 c 
5.  5 2 
 6a b 
3.
n3
n 1
6.
16 x6 y 7 z 8
2 x 4 y 4
0
Worksheet: Dividing Monomials
Date ___________________
Name _____________________________
1. 28x2
2. 42x2
7x2
48x4
3. 24x4
4. 35x
32x4
45x
5.
9x
6.
6x8
7.
9.
108x3
90x7
8. 72x10
20x11
54x2
88x
10.
22x9
11.
-16x -10
21x3
-15x3
12. -49x12
42x3
48x6
13.
12x -3
42x4
14. -15x6
-30x6
-25x8
15. -16x12
16. 81x6
-36x7
-9x6
17.
180x
18.
-16x11
-120x
19. -60x2
96x12
14x11
20.
54x -6
90x11