Name Class Date. Division Equations
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1 Name Class Date Division Equations Modeling Essential question: How do you solve whole-number equations that contain division? 2-8 video tutor CC.6.EE.7 EXPLORE Division Equations Nolan and his two friends ate an entire pizza. Each person ate pieces. How many pieces were in the pizza to start with? A Let x represent the number of pieces in the pizza to start with. Number of pieces of pizza eaten by each person = Number of pieces in the pizza to start with Number of people = x To answer this question, you can solve the equation = x. B The number of pieces in the pizza to start with is divided into equal groups. Each person ate of the total number of pieces. C of the total number of pieces is so x =. D Fraction pieces and counters can be used to model the equation. Use a fraction piece to represent x or x. Use counters to represent. E How many pieces do you need to model the entire pizza? Complete the model by drawing more fraction pieces and counters. F Explain how the model shows the answer. There were pieces of pizza to start with. Chapter 2 85 Lesson 8
2 When an equation contains division, solve by multiplying both sides of the equation by the same number. Multiplication Property of Equality You can multiply both sides of an equation by the same number, and the two sides will remain equal. 2 CC.6.EE.7 EXAMPLE Using the Multiplication Property of Equality Solve each equation. A 5 x = 20 What number is x divided by? Multiply both sides of the equation by this number. x = 20 5 x = Multiply. Check: x 5 = 20 =? 20 Substitute for x. 5 =? 20 Divide on the left side. B 5 = r 2 What number is r divided by? Multiply both sides of the equation by this number. Check: 5 = r 2 = r Multiply. 5 = r 2 5 =? Substitute for r. 2 5 =? Divide on the right side. Chapter 2 86 Lesson 8
3 CC.6.EE.6 EXAMPLE Solving Problems with Division Equations For a music concert, Mrs. DeSoe has chosen 2 students to hand out programs as people enter the auditorium. She has divided the programs evenly into 2 bundles, one for each student. Each bundle contains 55 programs. How many programs did Mrs. DeSoe have printed for the concert? Write and solve an equation. Let x represent the total number of programs. Number of programs in each bundle = Total number of programs Number of students 55 = x 2 To answer the question, you can solve the equation 55 = x = 2 x x is divided by. 55 = x 2 both sides by 2. = x Mrs. DeSoe had a total of programs printed. REFLECT a. Explain how this figure models the equation x = 8. TRY THIS! Solve each equation. b. y 9 = 2 c. x = 2 d. 9 = w 9 y = x = w = Chapter 2 87 Lesson 8
4 practice Solve each equation.. n = 68 n =. 0 h = 5 h = 7. s = s = 2. a 6 = 27 a = = w 8 w = 8. 2 = m 9 m =. b = 9 7 b = 6. 7 = t 2 t = 9. z 6 = 8 z = For 0 5, write and solve an equation to answer each question. 0. The total cost of tickets to a professional basketball game was divided equally among 5 friends. If each person paid $2, what was the total cost of the tickets?. Students trying out for cheerleader at a school were divided into 6 equal groups to learn the routine. There were 8 people in each group. How many students tried out for cheerleader? 2. What division equation is modeled by the figure at the right? Find the solution of the equation.. The children who attended a youth fitness camp were separated into groups to use the various exercise equipment. Since there were eight pieces of equipment, they were placed in 8 groups. If there were children in each of the groups, how many children attended the fitness camp?. During a radio promotion, identical prize packages each included concert tickets. How many tickets were given away if there were 5 prize packages? 5. At Baker Middle School, there are 5 Spanish classes with 2 students in each class. There are French classes with 26 students in each class. How many students altogether are in the Spanish and French classes? Chapter 2 88 Lesson 8
5 Name Class Date 2-8 Additional Practice Solve each equation. Check your answers.. s v q 7. m x 6. n 8 7. t 8. p v 8 Solve each equation. Check your answers m 9. r x 7. 9 p 2. 5 d 5 5. n q 2 7. u w All the seats in the theater are divided into 6 groups. There are 5 seats in each group. Using the variable s, write and solve a division equation to find how many seats there are in the theater. 20. There are 6 ounces in one pound. A box of nails weighs pounds. Using the variable w, write and solve a division equation to find how many ounces the box weighs. Chapter 2 89 Practice and Problem Solving
6 Problem Solving Use the table to write and solve a division equation to answer each question.. How many total people signed up to play soccer in Bakersville this year? 2. How many people signed up to play lacrosse this year?. What was the total number of people who signed up to play baseball this year?. Which two sports in the league have the same number of people signed up to play this year? How many people are signed up to play each of those sports? Bakersville Sports League Number of Teams Players on Each Team Sport Baseball 7 20 Soccer 5 Football 8 2 Volleyball 2 9 Lacrosse 6 7 Basketball 0 0 Tennis 8 6 Circle the letter of the correct answer. 5. Which sport has a higher total number of players, football or tennis? How many more players? A football; 0 players B tennis; players C football; 8 players D tennis; 8 players 6. Only one sport this year has the same number of players on each team as its number of teams. Which sport is that? F basketball G football H soccer J tennis Chapter 2 90 Practice and Problem Solving
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