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

Warm Up Evaluate each expression. 1. (–7)(2.8) 2. 0.96 ÷ 6 3. (–9)(–9) 4. 5. 6.

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

Inverse Operations Operation Inverse Operation Solving an equation that contains or is similar to solving an equation that contains or . Use inverse operations to undo the operations on the . Inverse Operations Operation Inverse Operation

Example 1A: Solving Equations by Using Multiplication Solve the equation. –8 = j 3

Check It Out! Example 1a Solve the equation. Check your answer. = 10 p 5 Since p is divided by 5, multiply both sides by 5 to undo the division. To check your solution, substitute 50 for p in the original equation.

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

Check It Out! Example 1c Solve the equation. Check your answer. = 7 c 8 Since c is divided by 8, multiply both sides by 8 to undo the division. To check your solution, substitute 56 for c in the original equation.

Example 2A: Solving Equations by Using Division Solve the equation. Check your answer. 9y = 108

Example 2B: Solving Equations by Using Division Solve the equation. Check your answer. –4.8 = –6v Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.

Check It Out! Example 2a Solve the equation. Check your answer. 16 = 4c

Check It Out! Example 2b Solve the equation. Check your answer. 0.5y = –10

Check It Out! Example 2c Solve the equation. Check your answer. 15k = 75

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

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

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 To check your solution, substitute for z in the original equation. 3 2

Solve the equation. Check your answer. 1 4 1 5 – = b Check It Out! Example 3a Solve the equation. Check your answer. 1 4 1 5 – = b The reciprocal of is 5. Since b is multiplied by , multiply both sides by 5. 1 5 To check your solution, substitute – for b in the original equation. 5 4

Check It Out! Example 3b Solve the equation. = 4j 6 2 3

Check It Out! Example 3b Continued Solve the equation. = 4j 6 2 3

Check It Out! Example 3c Solve the equation. 1 w = 102 6

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.

Write an equation to represent the relationship. Check it Out! Example 4 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 Write an equation to represent the relationship.

Lesson Quiz: Part 1 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6. Solve each equation. 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6.

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