d ividing m onomials chapter 8.2. d ividing m onomials lesson objective: ncscos 1.01 write...
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D IVIDING M ONOMIALS Example 1- Simplify: x 4 x 2 Remember: x 4 = x * x * x * x which can also be written as xxxx Therefore x 4 = xxxx x 2 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: x 2 Rule: When dividing monomials you must subtract the exponents on the bottom from those on the top.TRANSCRIPT
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DIVIDING MONOMIALSChapter 8.2
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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.
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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.
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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
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DIVIDING MONOMIALS
Your turn to try!x3
x2
x5 x3
x3
x3
x3
x6
x3
x7
1.
2.
3.
4.
5.
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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
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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
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DIVIDING MONOMIALS
1. 4x3
2x
2. 9x5
3x2
3. 8x7
24x4
More Practice4x3
6x
12x3
2x6
4.
5.
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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
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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
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DIVIDING MONOMIALS Example 3- Therefore: x4 3
x2
Write out x2 three times
= (x2)3
(x2)(x2)(x2) =
x6
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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
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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
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DIVIDING MONOMIALS1.
2.
3.
4.
2
3
5
PRACTICE
y3
x2 3
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DIVIDING MONOMIALS1.
2.
3.
4.
2
3
5
PRACTICE
y3
x2 3
x6
x3
x10
x6
y9
1
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DIVIDING MONOMIALS Example 5 Simplify:
Solve each variable separately:
x3y3
x2y5y3
y5x3
x2
x 1y2
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DIVIDING MONOMIALS Put it all back together x 1
y2
xy2
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DIVIDING MONOMIALS1.
2.
3.
4.
x3y3
x2y2
x5y3
x2y5
6xy6
3x3y2
5x8y8
15x4y5
Practice
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DIVIDING MONOMIALS1.
2.
3.
4.
x3y3
x2y2
x5y3
x2y5
6xy6
3x3y2
5x8y8
15x4y5
xy
x3
y2
2y4
x2
x4y3
3
Practice
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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
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DIVIDING MONOMIALS1.
2.
3.
3x5 + 6x4 + 12x3
6x5 – 10x4 + 22x3
12x4 + 6x3 – 16x2
3x3
2x2
6x2
More Practice
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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
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DIVIDING MONOMIALS1.
2.
3.2
QUIZ 8.2x3x5
8x6
3x3
4x3
x2 5.
4. 6x6y2
3x3y5
24x5 + 12x3 – 18x2 3x2
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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