DIVIDING MONOMIALS
Chapter 8.2
DIVIDING MONOMIALS
Lesson
Objective: NCSCOS 1.01
Write equivalent forms of
algebraic expressions to solve
problems.
Students
will know how to apply
the laws of exponents when they
divide monomials.
DIVIDING MONOMIALS

Example 1: Simplify

Remember:

Therefore:
DIVIDING MONOMIALS


Cross out all the x’s that
are both on the top and
the bottom
You’re left with x*x on
top, so your answer is:
Rule: When dividing monomials you must
subtract the exponents on the bottom from
those on the top.
DIVIDING MONOMIALS

Example 2:
Which number is bigger, the top or bottom?
 If there are more on the bottom, then the x’s will
be on the bottom
 There are three more x’s on the bottom, so the
answer is:

DIVIDING MONOMIALS
3
x
1. 2
x
3
x
2. 5
x
3
x
3. 3
x
3
x
4. 6
x
3
x
5. 7
x
DIVIDING MONOMIALS
3
x
1. 2
x
x
5
x
2. 3 x2
x
3
x
3. 3 1
x
3
x
4. 6
x
1
x3
3
x
5. 7
x
1
x4
DIVIDING MONOMIALS




Example 3: Simplify
Divide the numbers first
 Since the number on the top is bigger, we’ll
have numbers on the top
Divide the letters next
 Since the x’s are bigger on the top, then the
x’s will be on the top
Since all the numbers are on
the top, your answer is simply:
DIVIDING MONOMIALS
1. 4x3
2x
2. 9x5
3x2
3. 8x7
24x4
3
4. 4x
6x
3
5. 12x
2x6
DIVIDING MONOMIALS
1. 4x3 2x2
2x
2. 9x5
3x2
3. 8x7
24x4
3
4. 4x
6x
2x2
3
3x3
x3
3
3
5. 12x
2x6
6
x3
DIVIDING MONOMIALS


Example 4: Simplify:
Order of operations says to do what’s inside the
parenthesis first!
So we have:
DIVIDING MONOMIALS

Solve the problem
DIVIDING MONOMIALS

Example 5: Simplify:
First we look to see if we can reduce inside the
parenthesis
 In this example we can’t
 Therefore we have multiply the fraction by itself
to take care of the exponent outside

DIVIDING MONOMIALS


Remember when we multiply fractions we
multiply the top numbers together and then the
bottom numbers
Rule: When dividing monomials with and
exponent outside the fraction you must
reduce the fraction then distribute the
exponent to all the numbers inside the
parenthesis
DIVIDING MONOMIALS
2
1.
3
2.
5
3.
4.
x2
y3
3
DIVIDING MONOMIALS
1.
2.
x6
3
1
x3
5
3.
4.
2
x2
y3
x10
3
x6
y9
DIVIDING MONOMIALS

Example 6: Simplify:

We will look at each letter separately
DIVIDING MONOMIALS

Set up a fraction

Which x is bigger?

By how much?

1, so there will be 1x on the top
DIVIDING MONOMIALS

Which y is bigger?

By how much?

2, so there will be 2 y’s on the bottom

You can’t do anything else, so that’s your answer!
DIVIDING MONOMIALS
1.
x3y3
x2y2
2.
x5y3
x2y5
3.
6xy6
3x3y2
4.
5x8y8
15x4y5
DIVIDING MONOMIALS
x3y3
x2y2
xy
x5y3
x2y5
x3
y2
3.
6xy6
3x3y2
2y4
x2
4.
5x8y8
15x4y5
1.
2.
x4y3
3
DIVIDING MONOMIALS


Example 7: Simplify
Divide each number from the top with the
number on the bottom:
DIVIDING MONOMIALS

Notice the signs in the middle stay the same!
DIVIDING MONOMIALS
1. 3x5 + 6x4 + 12x3
3x3
5 – 10x4 + 22x3
6x
2.
2x2
4 + 6x3 – 16x2
12x
3.
6x2
DIVIDING MONOMIALS
1. 3x5 + 6x4 + 12x3
3x3
5 – 10x4 + 22x3
6x
2.
2x2
3.
12x4
+
6x3
6x2
–
16x2
x2 + 2x + 4
3x3 – 5x2 + 11x
2x2
8
+x+ 3
DIVIDING MONOMIALS
5
x
1.
x3
8x6
2.
4x3
3.
2
3
3x
x2
6y2
6x
4.
3x3y5
5 + 12x3 – 18x2
24x
5.
3x2
DIVIDING MONOMIALS
5
x
1.
x3
8x6
2.
4x3
3.
2
3
3x
x2
x2
2x2
9x2
6y2
6x
4.
3x3y5
2x3
y3
5 + 12x3 – 18x2
24x
5.
3x2
8x3 + 4x – 6