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3.6 Clearing an Equation of
Fractions
• Goal: To solve an equation with fractions
we can use the “trick” of clearing the
fractions.
World’s Easiest Problem
2
1
5
x  x   2x
3
2
6
World’s Greatest Trick
• Anytime you see fractions in the equation
multiply every term of your equation by the
LCD.
Recap on LCD
• LCD : Least Common Denominator
• How do you find it? Take all the
denominators and take the Least Common
Multiple
• Least Common Multiple is the number that
all the numbers could be multiplied by
another number to get.
STEPS:
1) Multiply both sides of the equation by
the LCD to clear the fractions
2) Simplify by cross canceling
3) Distribute.
4) Collect like terms on same side.
5) Move variables to same side of
equation with the APE
5) Move the numbers (constants) to the
other side of the equation with the APE
6) Use the MPE to solve for the variable
What number are we going to
multiply by? (LCD)
2
1
5
x  x   2x
3
2
6
2
1
5
x
x 
 2x
3
2
6
4 x  3x   5  12 x 
 7 x  7 x  5  12 x  7 x
 5  0  5  5x  5
 5  5x
1

x
5
5
By what number would you
multiply to clear the fraction?
1
3
x2 x
4
4
LCD = 4
1
3
x2 x
4
4
x  8  3x
X=4
What is the LCD?
g 2 3
   2g
3 5 2
30 1g 30 2 30 3 30 2 g
      
1 3 1 5 1 2 1 1
10
6
15
30 1g 30 2 30 3 30 2 g
      
1 3 1 5 1 2 1 1
1
1
1
Write the equivalent equation
10 g  12  45  60 g
10g +12 =45 -60g
+60 g
+60 g
70 g + 12 = 45
-12 -12
- Add 60g to both sides
to get the variables on
the same side
- Subtract 12 from both
sides to get the numbers on
the same side
70 g = 33 - Divide both sides by
70 to solve for g
70
70
g= 33/70
Solve: You try
1
1 3
p 
3
6 2
Solve:  1
1
 3
6 p    6 
6
3
2
2p 1  9
-1
1

2
-1
2p  8
p4
1

2
Assignment:
Page 140
# 2-18 even
(2-6 just state the LCD
do not solve, 8-18 solve)
SHOW the Steps