ACTIVITY: Using Division to Solve Equations. Work with a partner. Use algebra tiles to model and solve the equation. a. 3x = 12
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1 . Solving Equations Using Multiplication or Division to solve equations? How can you use multiplication or division ACTIVITY: Using Division to Solve Equations Work with a partner. Use algebra tiles to model and solve the equation. a. = Model the equation =. Your goal is to get one variable tile by itself. Because there are variable tiles, divide the tiles into equal groups. Circle the groups. Keep one of the groups. This shows the value of. So, =. b. k = 8 c. = t d. 0 = m e. h = 6 ACTIVITY: Writing and Solving Equations Work with a partner. Write an equation shown by the algebra tiles. Then solve. Solving Equations In this lesson, you will solve equations using multiplication or division. solve real-life problems. a. c. b. d. 0 Chapter Epressions and Equations
2 ACTIVITY: Using a Different Method to Find a Solution Math Practice Analyze Givens How can you use the given information to decide which equation represents the situation? Work with a partner. Choose the equation you can use to solve each problem. Solve the equation. Then eplain how to solve the problem without using an equation. How are the two methods related? a. For the final part of a race, a handcyclist travels feet each second across a distance of 00 feet. How many seconds does it take for the handcyclist to travel the last 00 feet of the race? = = = = b. The melting point of the element radon is about 96 F. The melting point of nitrogen is about.6 times the melting point of radon. What is the melting point of nitrogen?.6 = =.6.6 = =.6 c. This year, a hardware store has a profit of $6.0 million. This profit is of last year s profit. What is last year s profit? 6 = 6 = + = 6 = 6. IN YOUR OWN WORDS How can you use multiplication or division to solve equations? Give an eample of each. Use what you learned about solving equations to complete Eercises 7 0 on page 06. Section. Solving Equations Using Multiplication or Division 0
3 . Lesson Lesson Tutorials Multiplication Property of Equality Words Multiplying each side of an equation by the same number produces an equivalent equation. Algebra If a = b, then a c = b c. Remember Multiplication and division are inverse operations. Division Property of Equality Words Dividing each side of an equation by the same number produces an equivalent equation. Algebra If a = b, then a c = b c, c 0. EXAMPLE Solving Equations a. Solve = 6. Undo the division. = 6 Write the equation. = ( 6) Multiplication Property of Equality = 8 Simplify. The solution is = 8. Check = 6 8 =? 6 6 = 6 b. Solve 8 = y. Undo the multiplication. 8 = y Write the equation. 8 = y. = y Simplify. The solution is y =.. Division Property of Equality Check 8 = y 8 =? (.) 8 = 8 Eercises 7 8 Solve the equation. Check your solution.. =. a =. =.n 0 Chapter Epressions and Equations
4 EXAMPLE Solving an Equation Using a Reciprocal Solve = 8. = 8 Write the equation. Multiply each side by, the reciprocal of. ( ) = ( 8) = 0 The solution is = 0. Multiplicative Inverse Property Simplify. Eercises 9 Solve the equation. Check your solution.. =. 8 b = 6. 8 h = 9 0 F EXAMPLE Real-Life Application The record low temperature in Arizona is.6 times the record low temperature in Rhode Island. What is the record low temperature in Rhode Island? Words The record low in Arizona is.6 times the record low in Rhode Island. Record low temperature in Arizona Variable Let t be the record low in Rhode Island. Equation 0 =.6 t 0 =.6t 0.6 =.6t.6 = t Write equation. Division Property of Equality Simplify. The record low temperature in Rhode Island is F. Eercises 7 7. The record low temperature in Hawaii is 0. times the record low temperature in Alaska. The record low temperature in Hawaii is F. What is the record low temperature in Alaska? Section. Solving Equations Using Multiplication or Division 0
5 . Eercises Help with Homework. WRITING Eplain why you can use multiplication to solve equations involving division.. OPEN-ENDED Turning a light on and then turning the light off are considered to be inverse operations. Describe two other real-life situations that can be thought of as inverse operations. Describe the inverse operation that will undo the given operation.. multiplying by. subtracting. dividing by 8 6. adding 6 9+(-6)= +(-)= +(-9)= 9+(-)= Solve the equation. Check your solution. 7. h = 8. t = 9. n = 7 0. k = 9. m = 0. 8t =. 0. =.6. 0 = b. 6p = = 8d 7. n = 8.. = 0.6p.6 9. g = 0. 8 = c. 9 f =. 6 = 8 y. ERROR ANALYSIS Describe and correct the error in finding the solution.. =.. =. = Write the word sentence as an equation. Then solve.. A number divided by 9 is 6.. A number multiplied by is The product of and a number is The quotient of a number and. is. In Eercises 8 and 9, write an equation. Then solve. 8. NEWSPAPERS You make $0.7 for every newspaper you sell. How many newspapers do you have to sell to buy the soccer cleats? 9. ROCK CLIMBING A rock climber averages feet per minute. How many feet does the rock climber climb in 0 minutes? 06 Chapter Epressions and Equations
6 OPEN-ENDED (a) Write a multiplication equation that has the given solution. (b) Write a division equation that has the same solution REASONING Which of the methods can you use to solve c = 6? Multiply each side by. Multiply each side by. Multiply each side by, then divide each side by. Divide each side by.. STOCK A stock has a return of $.6 per day. Write and solve an equation to find the number of days until the total return is $ ELECTION In a school election, of the students vote. There are 6 ballots. Write and solve an equation to find the number of students. 7. OCEANOGRAPHY Aquarius is an underwater ocean laboratory located in the Florida Keys National Marine Sanctuary. Solve the equation = 6 to find the value of. 8. SHOPPING The price of a bike at Store A is the price at 6 Ź6 ft Store B. The price at Store A is $0.60. Write and solve an equation to find how much you save by buying the bike at Store A. 9. CRITICAL THINKING Solve m = 0. 7 In four days, your family drives of a trip. 0. Your rate of travel is the same throughout the trip. The total trip is 0 miles. In how many more days will you reach your destination? Subtract. (Section.).. 7. ( 8). ( ). MULTIPLE CHOICE Of the 0 apartments in a building, 7 have been scheduled to receive new carpet. What fraction of the apartments have not been scheduled to receive new carpet? (Skills Review Handbook) A B 8 Section. ms_red pe_00.indd 07 C 8 D Solving Equations Using Multiplication or Division 07 /0/ :9: PM
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