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To understand the concept and
procedure for
dividing
monomials it is suggested that you first
review the lesson on
multiplying monomials.
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Multiplying monomials is a two step process.
First the coefficients of each monomial are
multiplied as you would multiply any
two or more numbers.
And secondly, you follow the rules for
multiplying variables,
whether the variables are like or unlike.
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For example:
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(5a)(-2b) = -10ab
or...
(3x3)(2x2) = 6x3+2 = 6x5
and finally...
(2c2d)(3c4d2)(-5c4d3)
= -30c10d6 |
In division we follow the same two step process.
However, because multiplication and division are
inverse (opposite) operations, instead of
multiplying the coefficients of the monomials
we must divide them.
And secondly we must follow the rules for dividing variables,
which means that when dividing like
variables we must subtract the exponents
instead of adding them.
The best way to understand this is to
look at some examples...
Example #1
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(14x4)÷(2x2) = ?
First...divide the coefficients: 14÷2 = 7
Second...divide the variables: x4÷x2 = x4-2
= x2
So the answer is:
(14x4)÷(2x2) = 7x2 |
Example #2
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(-32x5y4)÷(-4x2y3) =
?
First...divide the coefficients: -32÷-4 = 8
Second...divide the variables: x5y4÷x2y3
= x5-2y4-3 = x3y
So the answer is:
(-32x5y4)÷(-4x2y3)
= 8x3y
(-32x5y4)÷(-4x2y3) =
?
First...divide the coefficients: -32÷-4 = 8
Second...divide the variables: x5y4÷x2y3
= x5-2y4-3 = x3y
So the answer is:
(-32x5y4)÷(-4x2y3)
= 8x3y
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Example #3
In this example we will see what happens when we divide monomials
which do not have like variables.
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(-12x3)÷(4y2) = ?
First...divide the coefficients: -12÷4 = -3
Second...if the variables are not like then the best we can
do is to leave them as a fraction:
x3÷y2 = x3/y2
So the answer is:
(-12x3)÷(4y2) = -3x3/y2 |
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