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AlgebraAlgebra
3.6 3.6
Clearing Fractions and Clearing Fractions and DecimalsDecimals
Clearing the fractionsClearing 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 fractionsClearing the fractions3
6 2 85x x
Clearing the fractionsClearing the fractions3
6 2 85x x To clear the fraction,
multiplyboth sides of the equation by the denominator of 5.
Clearing the fractionsClearing the fractions3
6 2 85x x
35 6 2 8 5
5x x
To clear the fraction, multiplyboth sides of the equation by the denominator of 5.
Clearing the fractionsClearing the fractions3
6 2 85x x
35 6 2 8 5
5x x
3 30 10 40x x
To clear the fraction, multiplyboth sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual
Clearing the fractionsClearing the fractions3
6 2 85x x
35 6 2 8 5
5x x
3 30 10 40x x
To clear the fraction, multiplyboth sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual
70 7x
Clearing the fractionsClearing the fractions3
6 2 85x x
35 6 2 8 5
5x x
3 30 10 40x x
To clear the fraction, multiplyboth sides of the equation by the denominator of 5.
The fraction is cleared. Solve as usual
70 7x10x
Clearing the fractionsClearing 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 fractionsClearing 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 fractionsClearing 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 fractionsClearing 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 fractionsClearing the fractions
2 3( 4) 2
3 4x x
Clearing the fractionsClearing the fractions
2 3( 4) 2
3 4x x The LCD of 3 and 4 is 12
Clearing the fractionsClearing 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 fractionsClearing 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 fractionsClearing 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 fractionsClearing 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 decimalsClearing 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 decimalsClearing the decimals
4x –.24 = .56 – .8x4x –.24 = .56 – .8x There are There are 22 places to places to the right of the the right of the
decimal point in 2 of the decimal point in 2 of the terms. So, multiply terms. So, multiply both both sides of the equation sides of the equation by by 110000..
100100 [4x - .24] = [.56 – .8x] [4x - .24] = [.56 – .8x] 100100
400x – 24 = 56 – 80x400x – 24 = 56 – 80x
480x = 80480x = 80
x = 1/6x = 1/6
Clearing the decimalsClearing the decimals
.005x + .02 = .01x – .025.005x + .02 = .01x – .025 There are There are 33 places to places to the right of the the right of the decimal point so decimal point so
multiply both sides of multiply both sides of the equation by the equation by 11000000..
10001000 [.005x + .02] = [.01x – .025] [.005x + .02] = [.01x – .025] 10001000
5x + 20 = 10x – 255x + 20 = 10x – 25
45 = 5x45 = 5x
x = 9x = 9
Try theseTry these1 1
53 2x x 1.
Try theseTry these1 1
53 2x x
Solution: x = -6
1.
Try theseTry these1 1
53 2x x
Solution: x = -6
2. . 75x + 5 = 2.5x – 2
1.
Try theseTry these1 1
53 2x x
Solution: x = -6
2. . 75x + 5 = 2.5x – 2 Solution: x = 4
1.
HomeworkHomework
Next year do some more on the hw Next year do some more on the hw with binomials In the numberatorwith binomials In the numberator
