Solving Equations by by Solving Equations Multiplying or Dividing Multiplying or Dividing Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Algebra 1 Solving Equations by Multiplying or Dividing Warm Up Evaluate each expression. 1. (–7)(2.8) 2. 0.96 ÷ 6 3. (–9)(–9) 4. 5. 6. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Objective Solve one-step equations in one variable by using or . Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing 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 Holt McDougal Algebra 1 Inverse Operation Solving Equations by Multiplying or Dividing Example 1A: Solving Equations by Using Multiplication Solve the equation. j –8 = 3 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 1a Solve the equation. Check your answer. p = 10 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. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 1b Solve the equation. Check your answer. y –13 = 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. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 1c Solve the equation. Check your answer. c =7 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. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Example 2A: Solving Equations by Using Division Solve the equation. Check your answer. 9y = 108 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Example 2B: Solving Equations by Using Division Solve the equation. Check your answer. –4.8 = –6v Holt McDougal Algebra 1 Since v is multiplied by –6, divide both sides by –6 to undo the multiplication. Solving Equations by Multiplying or Dividing Check It Out! Example 2a Solve the equation. Check your answer. 16 = 4c Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 2b Solve the equation. Check your answer. 0.5y = –10 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 2c Solve the equation. Check your answer. 15k = 75 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing 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 . Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Example 3A: Solving Equations That Contain Fractions Solve the equation. 5 w = 20 6 The reciprocal of 5 is 6 . Since w is 6 5 5 multiplied by , multiply both sides 6 6 by . 5 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Example 3B: Solving Equations That Contain Fractions Solve the equation. 3 = 1 z 16 8 The reciprocal of 1 is 8. Since z is 8 1 multiplied by , multiply both sides 8 by 8. To check your solution, substitute 3 for z in the 2 original equation. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 3a Solve the equation. Check your answer. 1 – 1 = b 5 4 The reciprocal of 1 is 5. Since b is 5 1 multiplied by , multiply both sides 5 by 5. To check your solution, substitute – 5 for b in the 4 original equation. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 3b Solve the equation. 4j = 2 3 6 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 3b Continued Solve the equation. 4j = 2 3 6 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Check It Out! Example 3c Solve the equation. 1 w = 102 6 Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Example 4: Application Ciro puts 1 4 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. one-fourth times earnings equals college fund Write an equation to represent the relationship. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing 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. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Lesson Quiz: Part 1 Solve each equation. 1. 2. 3. 8y = 4 4. 126 = 9q 5. 6. Holt McDougal Algebra 1 Solving Equations by Multiplying or Dividing Lesson Quiz: Part 2 9 7. A person's weight on Venus is about his or 10 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. Holt McDougal Algebra 1