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SOLVING EQUATIONS CONTAINING
FRACTIONS AND DECIMALS
Clearing the fractions
It is easier to deal with whole numbers in an equation than with fractions.
To clear the fractions out of the equation, follow these STEPS:
1. Identify all the fractions in the equation that are not inside grouping symbols.
2. Find the LCD of these fractions. 3. Multiply both sides of the equation by the
LCD. 4. Solve as usual.
Clearing the fractions 3
6 2 85
x x
Clearing the fractions 3
6 2 85
x x To clear the fraction, multiply both sides of the equation by the denominator of 5.
Clearing the fractions 3
6 2 85
x x
3
5 6 2 8 55
x x
To clear the fraction, multiply both sides of the equation by the denominator of 5.
Clearing the fractions 3
6 2 85
x x
3
5 6 2 8 55
x x
3 30 10 40x x
To clear the fraction, multiply both sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual
Clearing the fractions 3
6 2 85
x x
3
5 6 2 8 55
x x
3 30 10 40x x
To clear the fraction, multiply both sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual
70 7x
Clearing the fractions 3
6 2 85
x x
3
5 6 2 8 55
x x
3 30 10 40x x
To clear the fraction, multiply both sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual
70 7x
10x
Clearing the fractions
3 14 8
5 2x x
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Clearing the fractions
3 110 4 8 10
5 2x x
3 14 8
5 2x x
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Multiply both sides of the equation by the LCD of 10. You must distribute to each term on both sides!
Clearing the fractions
3 110 4 8 10
5 2x x
3 14 8
5 2x x
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Multiply both sides of the equation by the LCD of 10. You must distribute to each term on both sides!
6 40 5 80x x The fractions are cleared. Now, solve as usual.
Clearing the fractions
3 110 4 8 10
5 2x x
3 14 8
5 2x x
Find the LCD of the fractions in the equation. What is the LCD of 5 and 2?
Multiply both sides of the equation by the LCD of 10. You must distribute to each term on both sides!
6 40 5 80x x The fractions are cleared. Now, solve as usual.
40x
Clearing the fractions
2 3( 4) 2
3 4x x
Clearing the fractions
2 3( 4) 2
3 4x x
The LCD of 3 and 4 is 12
Clearing the fractions
2 3( 4) 2
3 4x x
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
2 312 ( 4) 2 12
3 4x x
Clearing the fractions
2 3( 4) 2
3 4x x
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
8( 4) 24 9x x The fractions are cleared. Now, solve as usual.
2 312 ( 4) 2 12
3 4x x
Clearing the fractions
2 3( 4) 2
3 4x x
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
8( 4) 24 9x x The fractions are cleared. Now, solve as usual.
2 312 ( 4) 2 12
3 4x x
8 32 24 9x x
Clearing the fractions
8x
2 3( 4) 2
3 4x x
The LCD of 3 and 4 is 12
Multiply both sides of the equation by the LCD of 12.
8( 4) 24 9x x The fractions are cleared. Now, solve as usual.
2 312 ( 4) 2 12
3 4x x
8 32 24 9x x
Clearing the decimals It is easier to deal with whole numbers in an
equation than with decimals.
To clear the decimals out of the equation, follow these STEPS:
1. Identify all the decimals in the equation that are not inside grouping symbols.
2. Find the term with the most digits to the right of the decimal point.
3. Multiply both sides of the equation by the power of 10 that will make that term a whole number.
4. Solve as usual.
Clearing the decimals
4x –.24 = .56 – .8x There are 2 places to
the right of the decimal point in 2 of the terms. So, multiply both sides of the equation by 100.
100 [4x - .24] = [.56 – .8x] 100
400x – 24 = 56 – 80x
480x = 80
x = 1/6
Clearing the decimals
.005x + .02 = .01x – .025 There are 3 places to
the right of the decimal point so multiply both sides of the equation by 1000.
1000 [.005x + .02] = [.01x – .025] 1000
5x + 20 = 10x – 25
45 = 5x
x = 9
Try these 1)
1
3x + 5 = -
1
2x
2) 0.75x + 5 = 2.5x – 2
x = -6
x = 4
Homework
Worksheet
Study for fraction quiz Thursday
Study for Unit 3 quiz Thursday
