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Holt McDougal Algebra 1

Solving Equations by

Multiplying or Dividing Solving Equations by

Multiplying or Dividing

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz





Warm Up

Evaluate each expression.

1. (–7)(2.8)

2. 0.96 ÷ 6

3. (–9)(–9)

4.

5.

6.

19.6

0.16

1

81

2 3

1.8




Solve one-step equations in one variable by

using multiplication or division.

Objective




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.




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 = j

3

–8 –24

3

Check –8 = j

3




Solve the equation.

Example 1B: Solving Equations by Using

Multiplication

Since n is divided by 6,


to undo the division. n = 16.8

2.8 2.8


substitute 16.8 for n in the

original equation.

= 2.8 n

6

2.8 16.8

6

Check = 2.8 n

6




Solve the equation. Check your answer.

Check It Out! Example 1a

Since p is divided by 5,


to undo the division. p = 50

10 10


substitute 50 for p in the

original equation.

= 10 p

5

10 50

5

Check = 10 p

5





Check It Out! Example 1b

Since y is divided by 3,

multiply both sides by 3 to

undo the division. –39 = y

–13 –13


substitute –39 for y in the

original equation.

–13 = y

3

–13 –39

3

y Check –13 =

3





Check It Out! Example 1c

Since c is divided by 8,


to undo the division. c = 56

7 7


substitute 56 for c in the

original equation.

= 7 c

8

7 56

8

Check = 7 c

8





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


substitute 12 for y in the

original equation.

9y = 108

9(12) 108

Check 9y = 108





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


substitute 0.8 for v in the

original equation.

–4.8 = –6v

–4.8 –6(0.8)

Check –4.8 = –6v






Since c is multiplied by 4,


undo the multiplication. 4 = c

16 16


substitute 4 for c in the

original equation.

16 = 4c

16 4(4)

Check 16 = 4c






Since y is multiplied by 0.5,

divide both sides by 0.5 to

undo the multiplication. y = –20

–10 –10


substitute –20 for y in the

original equation.

0.5y = –10

0.5(–20) –10

Check 0.5y = –10






Since k is multiplied by 15,


undo the multiplication. k = 5

75 75


substitute 5 for k in the

original equation.

15k = 75

15(5) 75

Check 15k = 75




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.




Solve the equation.

Example 3A: Solving Equations That Contain

Fractions

w = 24

20 20


substitute 24 for w in the

original equation.

w = 20 5 6

Check w = 20 5

6

The reciprocal of is . Since w is

multiplied by , multiply both sides

by .

5 6

6 5

5 6

6 5

20




Solve the equation.

Example 3B: Solving Equations That Contain

Fractions

= z 3

16


substitute for z in the

original equation.

3 2

= z 3 2

1 8 The reciprocal of is 8. Since z is


by 8.

1 8

1 8

Check 1

8

3 16

= z

3

16

3

16






– = b 1 4


substitute – for b in the

original equation.

5 4

1 5

The reciprocal of is 5. Since b is


by 5.

1 5

1 5

= b 5 4

–

= b 5 4 Check 1 1 –





j = 1

Solve the equation.

= 4j 6

2 3

is the same as j. 4 6

4j

6

The reciprocal of is . Since j is


by .

4 6

4 6

6 4

6 4




Check It Out! Example 3b Continued


substitute 1 for j in the

original equation.

Check 2

3

4j 6

=

Solve the equation.

= 4j 6

2 3




w = 712

102 102


substitute 712 for w in the

original equation.

w = 102 1 6

Check w = 102 1

6

The reciprocal of is 6. Since w is


by 6 .

1 6

1 6

Solve the equation.


102




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.

1 4

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.




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.




WORDS

Addition Property of Equality

You 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




WORDS

Subtraction Property of Equality

You 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





WORDS

Multiplication Property of Equality

You 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 Division Property of Equality

You 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 8

4

8

4 =

a c

a c

=




Lesson Quiz: Part 1

Solve each equation.

1.

2.

3. 8y = 4

4. 126 = 9q

5.

6.

21

2.8

–14

40




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.

9

10

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