Clearing Fractions

Goal: To solve an equation with fractions by first clearing the fractions.

xxx 26

5

2

1

3

2

Anytime you see Fractions in the equation multiply every term of your equation by the 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.

I look for the largest denominator and see if it is multiple by the other denominators

If it is multiple by the rest of the denominators then I am done

If its not a multiple of the denominators then I multiply my largest denominator by 2 or 3 and keep doing the process until I find a number that is a multiple of all denominators

1) Multiply both sides to clear fractions and decimals, if necessary

2) Distribute. 3) Collect like terms on same side.4) Move variables to same side of

equation with the APE5) Move the numbers (constants) to

the other side of the equation with the APE

6) Use the MPE to solve for the variable

xxx 26

5

2

1

3

2

xxx 12534

xx 1257 x7 x7

x550 5 5x55

x 1 5 5

(2/3x) (6/1) +(1/2x) (6/1) = (5/6) (6/1) + (2x)(6)

(12x /3) + (6x /2) = (30/6) + (12x)

xx4

32

4

1

LCD = 4

Write the equivalent equation

xx 38

1

1

4 1 4 34 2

1 4 1 4

x x

1

1

- Subtract x from both sides to get the variables on the same side

- Divide by 2 to solve for x

- X=4

x +8 =3x-x -x

8= 2x

22

4=x

(1g/3) + (2/5) = (3/2) - 2g

What is the LCD?30

30 1 30 2 30 3 30 2

1 3 1 5 1 2 1 1

g g

Write the equivalent equation

gg 60451210

30 1 30 2 30 3 30 2

1 3 1 5 1 2 1 1

g g

10

1

6

1

15

1

+60 g+60 g- Add 60g to both sides to get the variables on

the same side

70 g + 12 = 45 - Subtract 12 from both sides to get the numbers on

the same side-12 -12

70 g = 33 - Divide both sides by 70 to solve for g

70 70g= 33/70

2

3

6

1

3

1p

2

36

6

1

3

16 p

912 p- 1- 1

82 p2

1

2

1

4p

Algebra Review