Carson Elementary And Intermediate Algebra 3e

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Carson Elementary and Intermediate Algebra 3e
Section 2.3.3
Objectives
1.
Use the multiplication principle to clear fractions and decimals from equations.
Vocabulary
Prior Knowledge
Use the addition and multiplication property of equality to solve linear equations.
New Concepts
1. Clearing Fractions
Notice what happens in this arithmetic problem:
5
8
13
7
7
7
When we multiply each term by the LCD, which is 7, we get an equivalent equation
5
8
13
7
7
7
7
7
7
5
8
13
This is still a true statement but we have eliminated the fractions. This is the process of clearing the
fraction. You must multiply EVERY TERM by the LCD, even if the term does not contain a fraction.
We can do this only because it is an equation!
Example 1:
2
x
1
1
4
LCD = 18
6
9
2
x
1
1
 
18
4
18
18
Multiply each term by 18
6
9
72 – 3(2x+1) = 2
Reduce each fraction - this eliminates the denominators
and the problem becomes a regular linear equation
72 – 6x – 3 = 2
Distributive property to remove parentheses.
Be careful to distribute the minus sign correctly!!
-6x + 69 = 2
Combine like terms
-6x = -67
Subtract 69 from both sides.
67
x 
Divide both sides by -6.
6
V Zabrocki 2010
page 1

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