2-2 Solving Equations by Multiplying or Dividing

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

2-2 Solving 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

2-2 Solving Equations by Multiplying or Dividing

Prep for MA.912.A.3.2 Identify and apply the…properties of equality.Also Prep for MA.912.A.3.1.

Sunshine State Standards

2-2 Solving Equations by Multiplying or Dividing

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

Objective

2-2 Solving Equations by Multiplying or Dividing

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.

Remember that an equation is like a balanced scale. To keep the balance, whatever you do on one side of the equation, you must also do on the other side.

2-2 Solving Equations by Multiplying or Dividing

Solve the equation.

Additional 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

2-2 Solving Equations by Multiplying or Dividing

Solve the equation.

Additional 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

2-2 Solving 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

2-2 Solving 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

2-2 Solving 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

2-2 Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Additional 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

2-2 Solving Equations by Multiplying or Dividing

Solve the equation. Check your answer.

Additional 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

2-2 Solving 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

2-2 Solving 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

2-2 Solving 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

2-2 Solving 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.

2-2 Solving Equations by Multiplying or Dividing

Solve the equation.

Additional 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

2-2 Solving Equations by Multiplying or Dividing

Solve the equation.

Additional 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

2-2 Solving 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–

2-2 Solving Equations by Multiplying or Dividing

Check It Out! Example 3b

j = 1

Solve the equation. Check your answer.

=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

2-2 Solving 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. Check your answer.

=4j6

23

2-2 Solving Equations by Multiplying or Dividing

w = 612

102 102

To check your solution, substitute 612 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 your answer.Check It Out! Example 3c

( )1 612 102

6

2-2 Solving Equations by Multiplying or Dividing

Additional 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.

2-2 Solving 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.

2-2 Solving Equations by Multiplying or Dividing

2-2 Solving Equations by Multiplying or Dividing

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz: Part ISolve each equation.

1.

2.

3. 8y = 4

4. 126 = –9q

5.

6.

21

2.8

–14

40

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz: Part II

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

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz for Student Response Systems

1. Solve the equation.

A. y = 0.0045

B. y = 0.045

C. y = 0.45

D. y = 4.5

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz for Student Response Systems

2. Solve the equation.

A. a = –24

B. a = –10

C. a = –2

D. a = 24

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz for Student Response Systems

3. Solve the equation.

A.

B.

C. f = 2

D. f = 3

6f = 2

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz for Student Response Systems

4. Solve the equation.

A. v = –60

B. v = –30

C. v = 30

D. v = 60

150 = –5v

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz for Student Response Systems

5. Solve the equation.

A. p = –12

B. p = –6

C. p = 6

D. p = 12

2-2 Solving Equations by Multiplying or Dividing

Lesson Quiz for Student Response Systems

6. A boy’s weight on the moon is about his

weight on Earth. Identify the equation

that shows how much the boy weighs on

Earth if he weighs 15 pounds on the

moon.

A.

B.

C.

D.