Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying...

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Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson Lesson Presentation Presentation Lesson Quiz Lesson Quiz

Transcript of Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying...

Page 1: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing2-2 Solving Equations by

Multiplying or Dividing

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Page 2: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Warm UpEvaluate each expression. 1. (–7)(2.8)

2. 0.96 ÷ 6

3. (–9)(–9)

4.

5.

6.

19.6

0.16

1

81

23

1.8

Page 3: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve one-step equations in one variable by using multiplication or division.

Objective

Page 4: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Inverse Operations

Operation Inverse Operation

Multiplication Division

Division Multiplication

Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable.

Page 5: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 1A: Solving Equations by Using Multiplication

Since j is divided by 3, multiply both sides by 3 to undo the division.–24 = j

–8 –8

To check your solution, substitute –24 for j in the original equation.

–8 =j3

–8 –243

Check –8 =j3

Page 6: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 1B: Solving Equations by Using Multiplication

Since n is divided by 6, multiply both sides by 6 to undo the division.n = 16.8

2.8 2.8

To check your solution, substitute 16.8 for n in the original equation.

= 2.8n6

2.8 16.86

Check = 2.8n6

Page 7: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 1a

Since p is divided by 5, multiply both sides by 5 to undo the division.p = 50

10 10

To check your solution, substitute 50 for p in the original equation.

= 10p5

10 505

Check = 10p5

Page 8: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 1b

Since y is divided by 3, multiply both sides by 3 to undo the division.–39 = y

–13 –13

To check your solution, substitute –39 for y in the original equation.

–13 =y3

–13 –393

yCheck –13 =

3

Page 9: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 1c

Since c is divided by 8, multiply both sides by 8 to undo the division.c = 56

7 7

To check your solution, substitute 56 for c in the original equation.

= 7c8

7 568

Check = 7c8

Page 10: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Example 2A: Solving Equations by Using Division

Since y is multiplied by 9, divide both sides by 9 to undo the multiplication.y = 12

108 108

To check your solution, substitute 12 for y in the original equation.

9y = 108

9(12) 108

Check 9y = 108

Page 11: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Example 2B: Solving Equations by Using Division

Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.

0.8 = v

–4.8 –4.8

To check your solution, substitute 0.8 for v in the original equation.

–4.8 = –6v

–4.8 –6(0.8)

Check –4.8 = –6v

Page 12: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 2a

Since c is multiplied by 4, divide both sides by 4 to undo the multiplication.

4 = c

16 16

To check your solution, substitute 4 for c in the original equation.

16 = 4c

16 4(4)

Check 16 = 4c

Page 13: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 2b

Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication.y = –20

–10 –10

To check your solution, substitute –20 for y in the original equation.

0.5y = –10

0.5(–20) –10

Check 0.5y = –10

Page 14: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Check It Out! Example 2c

Since k is multiplied by 15, divide both sides by 15 to undo the multiplication.k = 5

75 75

To check your solution, substitute 5 for k in the original equation.

15k = 75

15(5) 75

Check 15k = 75

Page 15: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

Page 16: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3A: Solving Equations That Contain Fractions

w = 24

20 20

To check your solution, substitute 24 for w in the original equation.

w = 2056

Check w = 2056

The reciprocal of is . Since w is

multiplied by , multiply both sides

by .

56

65

566

5

20

Page 17: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3B: Solving Equations That Contain Fractions

= z3

16

To check your solution,

substitute for z in the

original equation.

32

= z32

18

The reciprocal of is 8. Since z is

multiplied by , multiply both sides

by 8.

181

8

Check18

316

= z

316

316

Page 18: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.Check It Out! Example 3a

– = b14

To check your solution,

substitute – for b in the

original equation.

54

15

The reciprocal of is 5. Since b is

multiplied by , multiply both sides

by 5.

151

5

= b54–

= b5 4Check11–

Page 19: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Check It Out! Example 3b

j = 1

Solve the equation.

=4j6

23

is the same as j.46

4j6

The reciprocal of is . Since j is

multiplied by , multiply both sides

by .

464

6

64

64

Page 20: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Check It Out! Example 3b Continued

To check your solution,

substitute 1 for j in the

original equation.

Check23

4j6

=

Solve the equation.

=4j6

23

Page 21: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

w = 712

102 102

To check your solution, substitute 712 for w in the original equation.

w = 10216

Check w = 10216

The reciprocal of is 6. Since w is

multiplied by , multiply both sides

by 6 .

16

16

Solve the equation.Check It Out! Example 3c

102

Page 22: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Example 4: Application

Write an equation to represent the relationship.

Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year.

14

one-fourth times earnings equals college fund

m = $1140

Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division.

Ciro earned $1140 mowing lawns.

Page 23: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Check it Out! Example 4

Write an equation to represent the relationship.

The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began.

Distance divided by 3 equals height in thousands of feet

15 = h

Substitute 45 for d.

The plane was flying at 15,000 ft when the descent began.

Page 24: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

WORDS

Addition Property of EqualityYou can add the same number to both sides of an equation, and the statement will still be true.

NUMBERS

3 = 3 3 + 2 = 3 + 2 5 = 5

ALGEBRA a = b a + c = b + c

Properties of Equality

Page 25: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

WORDS

Subtraction Property of EqualityYou can subtract the same number from both sides of an equation, and the statement will still be true.

NUMBERS

7 = 7 7 – 5 = 7 – 5 2 = 2

ALGEBRA a = b a – c = b – c

Properties of Equality

Page 26: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

WORDS

Multiplication Property of EqualityYou can multiply both sides of an equation by the same number, and the statement will still be true.

NUMBERS

6 = 6 6(3) = 6(3) 18 = 18

ALGEBRA a = b ac = bc

Properties of Equality

Page 27: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Properties of EqualityDivision Property of EqualityYou can divide both sides of an equation by the same nonzero number, and the statement will still be true.

WORDS

a = b (c ≠ 0)

8 = 8

2 = 2

ALGEBRA

NUMBERS 84

84

=

ac

ac=

Page 28: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Lesson Quiz: Part 1Solve each equation.

1.

2.

3. 8y = 4

4. 126 = 9q

5.

6.

21

2.8

–14

40

Page 29: Holt Algebra 1 2-2 Solving Equations by Multiplying or Dividing 2-2 Solving Equations by Multiplying or Dividing Holt Algebra 1 Warm Up Warm Up Lesson.

Holt Algebra 1

2-2Solving Equations by Multiplying or Dividing

Lesson Quiz: Part 2

7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus.

910