solving equations containing fractions …...clearing the fractions 3 6 2 8 5 xx 5 6 2 8 5 3 > @...

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