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8/14/2019 Section 23b

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The Multiplication Principle of Equality

2.3b

3. Use the multiplication principle to clearfractions and decimals from equations.

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Review: Terms

1223 x Three terms

x x 3

28

5

2Three terms

9532

x Three terms

8/14/2019 Section 23b

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Review: Terms

3323

118

9

2 y y y Four terms

x x 21

43

125

31 Four terms

18146232 zz Four terms

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Review

51

5 1

7

17 1

4

312 93

1

3

26 42

1

8/14/2019 Section 23b

6/16

713

78

75

Clearing Fractions

713

778

775

7

5

1

1

1

1

1

1

8 13

Multip

ly EVERY TERM by the LCD, even if the termdoes not contain a fraction.

Equivalent equation but no fractions!!!

7

137

7

8

7

57

Distributive Property

Only works with EQUATIONS!9

8

6

5 Expression.Cant clear the fractions.

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Clearing Fractions

9

1

6

124 x

To Solve Linear Equations1. Clear the fractions.2. Simplify both sides of the equation as needed.

a. Distribute to clear parentheses.b. Combine like terms.

3. Use the addition principle so that all variable terms

are on one side of the equation.4. Use the addition principle so that all constants areon the other side.

5. Use the multiplication principle to isolate the

variable.

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Clearing Fractions

9

1

6

124 x

1. Clear fractions.2. Simplify3. Move the variable terms.4. Move the constants .5. Isolate the variable.

LCD: 18

91

186

1x2184183

1

418

2

1

Terms: 3

23672 x 2696 x

6969

676 x 66

6

67 x

Goal: Denominators = 1

Take the time to rewrite! 123

x 12

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Clearing Fractions 1. Clear fractions.2. Simplify3. Move the variable terms.4. Move the constants .5. Isolate the variable.

LCD: 12

Terms: 42

6

5

4

3

3

1 x x

2

1 212

6

512

4

312

3

112

x x

99

3

1

4

1

x 4 x x 1010

2469 x

336 x

66

6

33 x

2

11

241094 x x x x 44

2496 x

9 x

10 24

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Clearing Fractions 1. Clear fractions.2. Simplify3. Move the variable terms.4. Move the constants .5. Isolate the variable.

LCD: 10

Terms: 3 y52

5y103

3y51

y52

105y103

103y51

10

2

1

1

1

2

1

32 y

y y y 415362

y y 1562

1563 y

y y

66

213 y

213 y 33

7y

53 y y 4

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Decimals

25. Decimals are another way to write fractions!

100

25

1.10

1

055.1000

55

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Multiplying Powers of 10

1020 200

102 20

102. 2

Move decimal point one place.

10020 2000

1002 200

1002. 20

1002. 2. 10002. 2

Move decimal point two places.

Count the number of zeros andmove the decimal that many places.

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1. Clear fractions.2. Simplify3. Move the variable terms.4. Move the constants .5. Isolate the variable.

LCD: 100

Terms: 3

x . x .. 43027025060

Clearing Decimals

256

0

x x 43027150 x x 3012027150 x x 3030

1203150 x 150150

303 x 33

10 x

x 27 x 430

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1. Clear fractions.2. Simplify3. Move the variable terms.4. Move the constants .5. Isolate the variable.

LCD: 10

Terms: 4

t ..t . 140410650

Clearing Decimals

1

t t 44

6565

1414

5

0

t t 4410460105

t t 41006510

1006514 t

3514 t

14

35

t 2

5 52 .

If the problem starts with decimals,leave the answer in decimal form.

610 t 104 t 14

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Solve. 0.8 4(a 1) = 0.2 + 3(4 a )

a) 10

b) 7.4

c) 8.6

d) 20.6

2.3

8/14/2019 Section 23b

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Solve. 0.8 4(a 1) = 0.2 + 3(4 a )

a) 10

b) 7.4

c) 8.6

d) 20.6

2 3