Holt McDougal Algebra 1

1-3Solving Equations by Multiplying or Dividing1-3 Solving Equations by

Multiplying or Dividing

Holt Algebra 1

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Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Algebra 1

Holt McDougal Algebra 1

1-3Solving Equations by Multiplying or Dividing

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

Objective

Holt McDougal Algebra 1

1-3Solving 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.

Holt McDougal Algebra 1

1-3Solving 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 =j3

Holt McDougal Algebra 1

1-3Solving 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 =y3

Holt McDougal Algebra 1

1-3Solving 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

9y = 108

Holt McDougal Algebra 1

1-3Solving 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

0.5y = –10

Holt McDougal Algebra 1

1-3Solving 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.

Holt McDougal Algebra 1

1-3Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3A: Solving Equations That Contain Fractions

w = 24

w = 2056 The reciprocal of is . Since w is

multiplied by , multiply both sides

by .

56

65

566

5

Holt McDougal Algebra 1

1-3Solving Equations by Multiplying or Dividing

Solve the equation.

Example 3B: Solving Equations That Contain Fractions

= z3

16

= z32

18

The reciprocal of is 8. Since z is

multiplied by , multiply both sides

by 8.

181

8

Holt McDougal Algebra 1

1-3Solving 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.

Holt McDougal Algebra 1

1-3Solving 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

Holt McDougal Algebra 1

1-3Solving 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

Holt McDougal Algebra 1

1-3Solving 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

Holt McDougal Algebra 1

1-3Solving 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=

Holt McDougal Algebra 1

1-3Solving 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

Holt McDougal Algebra 1

1-3Solving 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