Solving Equations by Multiplying or 1 9 Dividing

Solving Equations by Multiplying or 1 -9 Dividing Vocabulary Multiplication Property of Equality Division Property of Equality

Solving Equations by Multiplying or 1 -9 Dividing Like addition and subtraction, multiplication and division are inverse operations. They “undo” each other. • ÷

Solving Equations by Multiplying or 1 -9 Dividing If a variable is divided by a number, you can often use multiplication to isolate the variable. Multiply both sides of the equation by the number.

Solving Equations by Multiplying or 1 -9 Dividing Additional Example 1: Using the Division Property of Equality Solve the equation h = 13. Check your answer. 2 h 2 = 13 (2) h 2 = 13(2) h = 26 Check h 2 Think: h is divided by 2, so multiply both sides by 2 to isolate h. = 13 26 ? = 13 2 ? 13 = 13 Substitute 26 for h. 26 is a solution.

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 1 A Solve the equation. Check your answer. X 5 = 30 x = 30(5) x = 150 Check: x 5 = 30 150 ? = 30 5 30 = 30

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 1 B Solve the equation. Check your answer. j÷ 8=9 j = 9(8) j = 72 Check: j÷ 8=9 ? 72 ÷ 8 = 9 9=9

Solving Equations by Multiplying or 1 -9 Dividing

Solving Equations by Multiplying or 1 -9 Dividing If a variable is multiplied by a number, you can often use division to isolate the variable. Divide both sides of the equation by the number.

Solving Equations by Multiplying or 1 -9 Dividing Additional Example 2: Solving an Equation by Division Solve the equation 51 = 17 x. Check your answer. Think: x is multiplied by 17, 51 = 17 x so divide both sides by 17 to 51 = 17 x isolate x. 17 17 3=x Check 51 = 17 x ? 51 = 17(3) ? 51 = 51 Substitute 3 for x. 3 is a solution.

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 2 A Solve each equation. Check your answer. 76 = 19 y y = 76 19 y=4 Check 76 = 19 y ? 76 = 19(4) 76 = 76

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 2 B Solve each equation. Check your answer. t · 12 = 180 t = 180 12 t = 15 Check t · 12 = 180 ? 15 · 12 = 180

Solving Equations by Multiplying or 1 -9 Dividing Additional Example 3: Health Application Trevor’s heart rate is 78 beats per minute. How many times does his heart beat in 10 seconds? Use the given information to write an equation, where b is the number of heart beats in 10 seconds. If you count your heart beats for 10 seconds and then multiply that by 6, you can find your heart rate in beats per minute.

Solving Equations by Multiplying or 1 -9 Dividing Additional Example 3 Continued Beats in 10 s times 6 b · 6 6 b = 78 6 6 b = 13 = beats per minutes = 78 Think: b is multiplied by 6, so divide both sides by 6 to isolate b. Trevor’s heart beats 13 times 10 seconds.

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 3 A A museum charges $7 person for admission. If a group paid a total of $105 for admission, how many people were in the group? 7 · p = 105 7 7 p = 15 There were 15 people in the group.

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 3 B During a stock car race, one driver is able to complete 68 laps in 1 hour. How many laps would he finish in 15 minutes? The number of laps in 15 min times 4 will give you the total number of laps in 1 hour.

Solving Equations by Multiplying or 1 -9 Dividing Check It Out: Example 3 B Continued x 4 = 68 4 x = 68 4 4 x = 17 He will finish 17 laps in 15 minutes.

Solving Equations by Multiplying or 1 -9 Dividing Lesson Quiz: Part I Solve the equation. Check your answer. 1. 12 = 4 x x = 3; 12 = 4 3 2. 18 z = 90 z = 5; 18 5 = 90 3. 12 = x 4 x = 48; 12 = x 4 4. 840 = 12 y y = 70; 840 = 12 70 5. h = 9 22 h = 198; 198 = 9 22

Solving Equations by Multiplying or 1 -9 Dividing Lesson Quiz: Part II 6. The cost of each ticket at the carnival was $0. 25. Li bought $7. 50 worth of tickets. How many tickets did she buy? 30