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**Multiplying or Dividing 1-3**

Solving Equations by Multiplying or Dividing 1-3 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

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

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**Inverse Operations Operation Inverse Operation**

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. Inverse Operations Operation Inverse Operation Multiplication Division Division Multiplication

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**Example 1A: Solving Equations by Using Multiplication**

Solve the equation. –8 = j 3 Since j is divided by 3, multiply both sides by 3 to undo the division. –24 = j

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Check It Out! Example 1b Solve the equation. Check your answer. –13 = y 3 Since y is divided by 3, multiply both sides by 3 to undo the division. –39 = y

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**Example 2A: Solving Equations by Using Division**

Solve the equation. Check your answer. 9y = 108 Since y is multiplied by 9, divide both sides by 9 to undo the multiplication. y = 12

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Check It Out! Example 2b Solve the equation. Check your answer. 0.5y = –10 Since y is multiplied by 0.5, divide both sides by 0.5 to undo the multiplication. y = –20

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**Remember that dividing is the same as multiplying by the reciprocal**

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.

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**Example 3A: Solving Equations That Contain Fractions**

Solve the equation. 5 w = 20 6 The reciprocal of is Since w is multiplied by , multiply both sides by 5 6 w = 24

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**Example 3B: Solving Equations That Contain Fractions**

Solve the equation. 3 1 8 = z 16 The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. 1 8 = z 3 2

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**one-fourth times earnings equals college fund**

Example 4: Application 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 Write an equation to represent the relationship. Substitute 285 for c. Since m is divided by 4, multiply both sides by 4 to undo the division. m = $1140 Ciro earned $1140 mowing lawns.

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**Properties of Equality 3 = 3 3 + 2 = 3 + 2 5 = 5 a = b a + c = b + c**

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

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**Properties of Equality 7 = 7 7 – 5 = 7 – 5 2 = 2 a = b a – c = b – c**

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

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**Properties of Equality 6 = 6 6(3) = 6(3) 18 = 18 a = b ac = bc**

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

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**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 = a c

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**Lesson Quiz: Part 1 1. 2. 21 3. 8y = 4 4. 126 = 9q 2.8 5. 6. –14 40**

Solve each equation. 1. 2. 3. 8y = 4 = 9q 5. 6. 21 2.8 –14 40

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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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