DIVIDING MONOMIALSChapter 8.2

DIVIDING MONOMIALSLesson 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: x4

x2

Remember: x4 = x * x * x * x which can also be written as xxxx

Therefore x4 = xxxx x2 xx

Cancel out the number of x’s on the top that are on the bottom xxxx xx

What you are left with is your solution: x2

Rule: When dividing monomials you must subtract the exponents on the bottom from those on the top.

Example:

Which number is bigger, the top or bottom? x’s will end up where there are more There are three more x’s on the bottom, so

the answer is:

x2

x5

1x3

DIVIDING MONOMIALS

Your turn to try!x3

x2

x5 x3

x3

x3

x3

x6

x3

x7

1.

2.

3.

4.

5.

DIVIDING MONOMIALS

Your turn to try!x3

x2

x3 x3

x3

x5

x3

x6

x3

x7

1.

2.

3.

4.

5.

x

x2

1x4

x3

1

1

DIVIDING MONOMIALS Example 2- Simplify: 4x5

2x3

Divide the numbers first: 4 ÷ 2 = 2 Divide the variables second: x5/x3 = x2

Put the numbers and letters back together for your answer: 2x2

Rule: When dividing monomials you divide the numbers and letter separately

DIVIDING MONOMIALS

1. 4x3

2x

2. 9x5

3x2

3. 8x7

24x4

More Practice4x3

6x

12x3

2x6

4.

5.

DIVIDING MONOMIALS

1. 4x3

2x

2. 9x5

3x2

3. 8x7

24x4

More Practice4x3

6x

12x3

2x6

4.

5.

2x2

2x2

3x3

3

6

x3

3

x3

DIVIDING MONOMIALS Example 3- Simplify: x4 3

x2

Order of operations says to do what’s inside the parenthesis first!

We can reduce the number inside the parenthesisx4

x2 = x2

DIVIDING MONOMIALS Example 3- Therefore: x4 3

x2

Write out x2 three times

= (x2)3

(x2)(x2)(x2) =

x6

Example 4: 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

x4

y3

2

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

x4

y32= x4

y3x4

y3x8= y6

DIVIDING MONOMIALS1.

2.

3.

4.

2

3

5

PRACTICE

y3

x2 3

DIVIDING MONOMIALS1.

2.

3.

4.

2

3

5

PRACTICE

y3

x2 3

x6

x3

x10

x6

y9

1

DIVIDING MONOMIALS Example 5 Simplify:

Solve each variable separately:

x3y3

x2y5y3

y5x3

x2

x 1y2

DIVIDING MONOMIALS Put it all back together x 1

y2

xy2

DIVIDING MONOMIALS1.

2.

3.

4.

x3y3

x2y2

x5y3

x2y5

6xy6

3x3y2

5x8y8

15x4y5

Practice

DIVIDING MONOMIALS1.

2.

3.

4.

x3y3

x2y2

x5y3

x2y5

6xy6

3x3y2

5x8y8

15x4y5

xy

x3

y2

2y4

x2

x4y3

3

Practice

DIVIDING MONOMIALS Example 6: Simplify: 4x4 – 8x3 + 6x2

2x2

Divide each number from the top with the number on the bottom:

– +

Notice that the sign between each number stays the same as the signs on the top of the problem

2x2

4x

3

DIVIDING MONOMIALS1.

2.

3.

3x5 + 6x4 + 12x3

6x5 – 10x4 + 22x3

12x4 + 6x3 – 16x2

3x3

2x2

6x2

More Practice

DIVIDING MONOMIALS1.

2.

3.

3x5 + 6x4 + 12x3

6x5 – 10x4 + 22x3

12x4 + 6x3 – 16x2

3x3

2x2

6x2

More Practice

x2 + 2x + 4

3x3 – 5x2 + 11x

2x2 + x +

83

DIVIDING MONOMIALS1.

2.

3.2

QUIZ 8.2x3x5

8x6

3x3

4x3

x2 5.

4. 6x6y2

3x3y5

24x5 + 12x3 – 18x2 3x2

DIVIDING MONOMIALS1.

2.

3.2

QUIZ 8.2x3x5

8x6

3x3

4x3

x2 5.

4. 6x6y2

3x3y5

24x5 + 12x3 – 18x2 3x2

x2

2x3

9x2

2x3

y3

8x3 + 4x – 6