Divide by a. One-Digit Divisor

Transcription

1 CHAPTER 3 Divide by a One-Digit Divisor connected.mcgraw-hill.com Investigate Animations Vocabulary Math Songs The BIG Idea How can I accurately divide by one-digit numbers when the division problem is shown in various ways? Multilingual eglossary Learn Personal Tutor Virtual Manipulatives Audio Make this Foldable to help organize information about division. Division Lesson 1 Divide by a One-Digit Divisor. Foldables Practice Self-Check Practice egames Worksheets Assessment 102 Review Vocabulary Fact Family familia de operaciones A group of related facts using the same numbers. 3 5 = = = = 5 Key Vocabulary English Español quotient cociente dividend dividendo divisor divisor

2 When Will I Use This? Your Turn! You will solve this problem in the chapter. Divide by a One-Digit Divisor 103

3 Are You Ready for the Chapter? You have two options for checking Prerequisite Skills for this chapter. Text Option Take the Quick Check below. Multiply $ $89 7. Turner s bookshelf has 6 shelves. Each shelf has 17 books. How many books are on the bookshelf? Round each number to its greatest place value $ , $33, $ $5, There are 7,209 students at the amusement park. Approximately how many students are at the park? Divide Three people spent a total of $24 for lunch. If they divide the total cost evenly, how much does each person pay? Item Cost Pizza $12 Salads $6 Drinks $6 Online Option Take the Online Readiness Quiz. 104 Divide by a One-Digit Divisor

4 Multi-Part Lesson 1 Divide by a One-Digit Divisor PART A B C D E Main Idea I will understand how division and multiplication are related. Vocabulary fact family Relate Division to Multiplication A fact family is a group of related facts that use the same numbers. You can use fact families to relate multiplication and division. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI Solve problems involving the division of twoand three-digit whole numbers by one- and two-digit whole numbers. BASKETBALL Sheryl is putting away 20 basketballs after practice. She places the balls on a rack that has 5 shelves. How many basketballs can she put on each shelf? Use a fact family. 5 4 = = = = 5 So, 20 5 = 4. Sheryl can put 4 basketballs on each shelf. Write a Fact Family Write a fact family for the counters shown. There are 5 rows, 9 columns, and a total of 45 counters = = = = 45 Lesson 1A Divide by a One-Digit Divisor 105

5 You can also use mental math to help you divide basic facts. Use Related Facts Check for reasonableness by comparing your answer to what was asked in the question. GIFT BAGS Ellie is creating gift bags for her party guests. She bought a total of 56 pencils that she wants to divide equally among the 7 gift bags. How many pencils will go in each bag? Find You can use a related multiplication fact to help you divide = Think What number times 7 is 56? 7 = 56 Write a related multiplication fact. 7 8 = 56 So, Ellie will put 8 pencils in each gift bag. Write a fact family for each set. See Examples 1 and , 8, , 7, 42 Divide. Use a related multiplication fact. See Example = = = = 9. 7 = = 11. There are 3 students playing a board game. The game contains 18 game pieces. If each student receives the same number of game pieces, how many pieces should each student receive? 12. E TALK MATH Explain how multiplication facts can help you divide. 106 Divide by a One-Digit Divisor

6 Write a fact family for each set. See Examples 1 and PRACTICE EXTRA Begins on page EP , 4, , 6, 36 Divide. Use a related multiplication fact. See Example = = = = = = 7 Orange blossoms have 5 petals and are some of the most fragrant flowers. 23. How many petals would there be in a group of 7 orange blossoms? 24. If you count 40 petals in all, what is the number of orange blossoms? 25. How many petals would there be in a group of 11 orange blossoms? 26. OPEN ENDED Write a real-world division problem that can be solved by using fact families. 27. REASONING Can the number 12 be part of more than one fact family? Explain. 28. WHICH ONE DOESN T BELONG? Identify the equation that does not belong with the other three. Explain = = = = E WRITE MATH Describe how you would find Lesson 1A Divide by a One-Digit Divisor 107

7 Multi-Part Lesson 1 PART Divide by a One-Digit Divisor A B C D E Division Models Main Idea I will explore division using models. Materials base-ten blocks You can use base-ten blocks to help you divide. In art class, three students share 48 markers evenly. How many markers will each student have? Find Step 1 Model 48 using base-ten blocks. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. Step 2 Divide the tens into 3 equal groups. Step 3 Regroup the remaining tens block into 10 ones. You now have 18 ones. Step 4 Divide the ones. There are 16 in each group. So, 48 3 = 16. Use multiplication to check your answer = Divide by a One-Digit Divisor

8 Model Remainders Find Step 1 Model 56 using base-ten blocks. Step 2 Divide the tens into 5 equal groups. Step 3 Divide the ones. There is one left over. When you divide 56 into 5 groups, there are 11 in each group with one left over. and Apply It Find each quotient using models. Tell how many are left over Kendrick has 42 craft sticks to make 3 identical crafts. How many sticks will he use for each craft? 10. E WRITE MATH Will 32 3 have any left over? Explain. Lesson 1B Divide by a One-Digit Divisor 109

9 Multi-Part Lesson 1 PART Divide by a One-Digit Divisor A B C D E Main Idea I will carry out division with and without remainders. Vocabulary dividend divisor quotient remainder Get ConnectED Divide a Two-Digit Dividend by a One-Digit Divisor In division, the dividend is the number that is being divided. The divisor tells you how many groups. dividend divisor The result of the division problem is called the quotient. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE BABYSITTING Mindy babysat on the weekend for 3 hours. If she made $36, how much did she make each hour? Find Step 1 Model 36. Step 2 Divide the tens ten in each group. Step 3 Divide the ones ones in each group. So, 36 3 = 12. Mindy made $12 every hour she babysat. 110 Divide by a One-Digit Divisor

10 A remainder is the number, or part left, after you divide. We use R to represent the remainder. BASEBALL Caleb is putting his baseball cards in an album. He has 57 cards and can put 4 cards on each page. How many full pages will Caleb have? Will there be any cards left? You need to find Step 1 Rewrite as Then divide the tens Divide with Remainders Divide. 5 4 = 1 Put 1 in the quotient over the tens place. Multiply. 4 1 = 4 Subtract. 5-4 = 1 Compare. 1 < 4 Write 57 4 as 4 57 to find the quotient. Step 2 Divide the ones. 14 R Bring down the ones. Divide = 4 Put 4 in the quotient over the ones place. Multiply. 4 4 = 16 Subtract = 1 Compare. 1 < 4 The remainder is = 14 R1 So, there will be 14 full pages and 1 card will be left over. Check for Reasonableness 14 4 = 56 and = 57. Divide Fill in each with the correct number to find So, 85 5 = Divide: 8 5 = 1 Subtract: 8-5 = 3 Multiply: 7 5 = 35 Lesson 1C Divide by a One-Digit Divisor 111

11 Divide. Use multiplication to check your answer. See Examples R R Five students volunteered to carry boxes. There are 62 boxes. Is it possible for each student to carry the same number of boxes and have all the boxes carried? Explain. 10. E TALK MATH Why is the remainder always less than the divisor? Divide. id Use multiplication li to check your answer. See Examples R PRACTICE EXTRA Begins on page EP2. 1 R Maranda practiced a total of 52 hours in 4 weeks to prepare for a piano recital. If she practiced the same number of hours each week, how many hours did she practice each week? 24. Lance is putting 75 photos in a scrapbook. If he puts 5 photos on each page, how many pages will he need? 112 Divide by a One-Digit Divisor

12 25. HIKING Alberto and Darcy are hiking in the Great Smoky Mountain National Park. One trail is about 68 miles long. Alberto and Darcy split the trip into 4 days of hiking. How many miles will they walk each day? 26. OPEN ENDED A two-digit dividend is divided by a one-digit divisor. The remainder is 2. Find possible values for the dividend and divisor. 27. NUMBER SENSE Use the digits 3, 6, and 9 one time each to write a division problem that contains a two-digit dividend. Write the division problem with the greatest quotient. 28. REASONING The following fact families show the relationship between multiplication and division = = =? 0? = 18 Explain why it is not possible to divide by zero. 29. E WRITE MATH Explain the meaning of a remainder in a division problem. Test Practice 30. A box of granola bars has 26 bars. If 7 friends split the bars evenly, how many bars will be left? A. 3 C. 5 B. 4 D An airplane that can hold 63 passengers is separated into 3 sections. Each section holds the same number of passengers. Which division sentence correctly describes the situation? F = 3 H = 5 G = 21 I = 7 Lesson 1C Divide by a One-Digit Divisor 113

13 Multi-Part Lesson 1 PART Divide by a One-Digit Divisor A B C D E Main Idea I will use basic facts and patterns to divide multiples of 10, 100, and 1,000 mentally. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE Division Patterns You can use basic facts and patterns to divide by multiples of 10. BUTTERFLIES A monarch butterfly can fly 240 miles in 3 days. Suppose it flies the same distance each day. How many miles can it fly each day? Since 240 is a multiple of 10, use the basic fact and continue the pattern = 8 basic fact = tens divided by 3 equals 8 tens Divide Multiples of 10 2,400 3 = hundreds divided by 3 equals 8 hundreds 24,000 3 = 8, thousands divided by 3 equals 8 thousands So, the butterfly can fly 80 miles each day. Find mentally. Divide Multiples of 10 Since 600 is a multiple of 10, you can use the basic fact and continue the pattern. 6 3 = 2 6 ones divided by 3 equals 2 ones = 20 6 tens divided by 3 equals 2 tens = hundreds divided by 3 equals 2 hundreds. So, = Divide by a One-Digit Divisor

14 MEASUREMENT A cow eats 900 pounds of hay over a period of 30 days. How many pounds of hay would the cow eat each day at this rate? You need to find Use the fact family of 3, 3, and 9 to help represent the problem. In multiplication, count the number of zeros in each factor. Write the zeros to the right of the product of the basic fact. 3 3 = = = = = = 30 This pattern suggests that you can cross out the same number of zeros in the dividend and the divisor to make division easier. 900/ 30/ Cross out the same number of zeros in both the dividend and divisor = 30 Divide. THINK: 9 tens 3 = 3 tens. So, = 30. The cow eats 30 pounds of hay each day. Divide mentally. See Examples , , A sailfish grabbed a fishing line and dragged it 300 feet in just 3 seconds. On average, how many feet did the fish drag the line each second? E 11. TALK MATH Explain how you know that the quotients 48 6 and are equal without doing any computation. Lesson 1D Divide by a One-Digit Divisor 115

15 Divide id mentally. See Examples , , , , A group of 10 people bought tickets to a reptile exhibit and paid a total of $130. What was the price of one ticket? 25. Measurement The fastest team in a wheelbarrow race traveled 100 meters in about 20 seconds. On average, how many meters did the team travel each second? 26. Measurement Daniela has a 160-ounce bag of potting soil. She puts an equal amount of soil in each pot shown. How much soil will she put in each pot? 27. A video store took in $450 in DVD rentals during one day. If DVDs rent for $9 each, how many DVDs were rented? PRACTICE EXTRA Begins on page EP OPEN ENDED Write a real-world division problem that can be solved by using basic facts or patterns. 29. NUMBER SENSE Write two different division problems that both have a quotient of FIND THE ERROR Sonia is finding 5, mentally. Find her mistake and correct it. 5,40/0/ 90/ 54 9 = E WRITE MATH Describe how placing zeros at the end of basic division facts helps you divide mentally. Write an example. 116 Divide by a One-Digit Divisor

16 School ol Bus Test Practice 32. An elementary school has 320 students. All of the students are going on a field trip. If 40 students can ride a bus, how many buses are needed? School Bus A. 5 C. 7 B. 6 D Petra and 5 of her friends have to hand out the number of fliers shown for the school play. If each person passes out the same number of fliers, how many fliers will Petra hand out? 34. There are 560 people in the auditorium. There are 70 rows of seats. Which number sentence describes the number of seats in each row? A = 392 B = 8 C = 70 D = SHORT RESPONSE Write two division sentences using the numbers below. 4, 17, 68 F. 15 H. 90 G. 20 I. 540 Divide. Use multiplication to check your answer. (Lesson 1C) A fisherman caught 42 fish over 3 days. If he caught the same number of fish each day, how many fish did he catch in one day? (Lesson 1C) Write a fact family for each set of numbers. (Lesson 1A) 41. 9, 6, , 4, , 6, , 7, 8 Lesson 1D Divide by a One-Digit Divisor 117

17 Multi-Part Lesson 1 Divide by a One-Digit Divisor PART A B C D E Problem-Solving Strategy: Guess, Check, and Revise Main idea I will solve problems by using the guess, check, and revise strategy. The Bactrian camel has two humps, while the Dromedary camel has just one. Toby counted 20 camels with a total of 28 humps. How many camels of each type are there? Understand What facts do you know? Bactrian camels have two humps. Dromedary camels have one hump. There are 20 camels with 28 humps. Plan What do you need to find? How many camels of each type are there? You can use the guess, check, and revise strategy to solve the problem. Use combinations of 20 total camels to guess. Solve Guess: 10 Bactrian camels and 10 Dromedary camels Check: 10 2 = 20 humps 20 humps + 10 humps = 30 humps 10 1 = 10 humps Too high. Revise: Guess: Try fewer Bactrian camels and more Dromedary camels. 7 Bactrian camels and 13 Dromedary camels Check: 7 2 = 14 humps 14 humps + 13 humps = 27 humps 13 1 = 13 humps Too low. Revise: Guess: Try more Bactrian camels and less Dromedary camels. 8 Bactrian camels and 12 Dromedary camels Check: 8 2 = 16 humps 16 humps + 12 humps = 28 humps 12 1 = 12 humps This guess is correct. So, there are 8 Bactrian camels and 12 Dromedary camels. Check Look back at the problem = 20 camels and = 28 humps. So, the answer is correct. GLE Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. 118 Divide by a One-Digit Divisor

18 Refer to the problem on the previous page. 1. Are there any other combinations of each type of camel that Toby could have seen? Explain your reasoning. 2. Suppose you saw 18 camels with a total of 22 humps. How many of each type did you see? 3. Explain how the guess, check, and revise method helped you solve this problem. 4. Explain why you should record your guesses and their results in the solve step of the problem-solving plan. PRACTICE EXTRA Begins on page EP2. Solve. Use the guess, check, and revise strategy. 5. Ruben sees 14 wheels on a total of 6 bicycles and tricycles. How many bicycles and tricycles are there? 6. Conner spent $66 on rookie cards and Hall of Famer cards. How many of each type of card did he buy? Baseball Card Cost Rookie 4 for $6 Hall of Famer 2 for $9 7. A teacher is having three students take care of 28 goldfish during the summer. He gave some of them to Alaina. Then he gave twice as many to Miguel. He gave twice as many to Kira as he gave to Miguel. How many fish did each student get? 9. Jerome bought 2 postcards and received $1.35 in change in quarters and dimes. If he got 6 coins back, how many of each coin did he get? 10. The sum of two numbers is 30. Their product is 176. What are the two numbers? 11. A tour director collected $258 for tour packages. Tour package A costs $18 and tour package B costs $22. How many of each tour package were sold? 12. Ticket prices for a science museum are shown in the table. If $162 is collected from a group of 12 people, how many adults and students are in the group? 8. Measurement Bike path A is 4 miles long. Bike path B is 7 miles long. If April biked a total of 37 miles, how many times did she bike each path? 13. E WRITE MATH Refer to Exercise 10. How did you use the guess, check, and revise strategy to find the numbers? To assess mastery of SPI , see your Tennessee Assessment Book. 119

19 Mission: Division Dividing Whole Numbers You will need: spinner, index cards Get Ready! Players: 2, 3, or 4 players Get Set! Each player makes a game sheet like the one shown at the right. Make a spinner as shown. All players find their quotients. The player with the greatest quotient earns one point. In case of a tie, each of those players earn one point. The first person to earn 5 points wins Go! The first person spins the spinner. Each player writes the number in one of the blanks on his or her game sheet. A zero cannot be placed as the divisor. Game Sheet The next person spins, and each player writes that number in a blank. The next player spins and each player fills in their game sheet. A player loses if he or she cannot use all the numbers. 120 Divide by a One-Digit Divisorisor

20 Mid-Chapter Check Divide. Use a related multiplication fact. (Lesson 1A) = = = = 5. 6 = = 8 7. Measurement The length of a rectangle can be found by dividing the area by the width. Find the length of the rectangle below. (Lesson 1C) area = 39 sq cm 3 cm 8. MULTIPLE CHOICE Suki received $87 for working 3 days. If she made the same amount each day, how much did Suki earn each day? (Lesson 1C) A. $20 C. $25 Divide mentally. (Lesson 1D) , , , MULTIPLE CHOICE A total of 180 students went on a field trip. There were 3 buses. If each bus had the same number of students on it, how many students were on each bus? (Lesson 1D) F. 6 G. 36 H. 54 I. 60 B. $29 D. $30 Divide. (Lesson 1C) Measurement The table shows the heights of the three tallest cacti. Find the height of each cactus in yards. (Hint: 1 yard = 3 feet) (Lesson 1C) Solve. Use the guess, check, and revise strategy. (Lesson 1E) 23. The sum of two numbers is 70. Their quotient is 13. What are the two numbers? 24. Rory has $1.30 in coins. If there is a total of 15 coins, how many quarters, dimes, nickels, and pennies does he have? Cactus Saguaro Organ-pipe Opuntia Height 75 ft 48 ft 33 ft 25. E WRITE MATH Can the remainder in a division problem ever equal the divisor? Explain. Mid-Chapter Check 121

21 Multi-Part Lesson PART 2 Divide Three- and Four-Digit Dividends A B C D E F Main Idea I will estimate quotients using rounding and compatible numbers. Vocabulary compatible numbers Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE Estimate Quotients To estimate a quotient, you can use compatible numbers, or numbers that are easy to divide mentally. Look for numbers that are part of fact families. DOGS A dog s heart beats 365 times in 3 minutes. About how many times does a dog s heart beat in 1 minute? Change 365 to 360 because 360 and 3 are compatible numbers = 120 Divide. So, a dog s heart beats about 120 times a minute. Check for Reasonableness = 360. Use a Compatible Dividend Estimate 3, Find a Compatible Divisor 3, ,200 8 Change 9 to 8 because 32 and 8 are compatible numbers. 3,200 8 = 400 Divide mentally. So, 3,200 9 is about 400. Check for Reasonableness = 3, Divide by a One-Digit Divisor

22 Use Rounding and Compatible Numbers To round 208 to the nearest ten, look at the number to the right of the tens place. Since 8 is 5 or greater, round up Estimate Step 1 Round the dividend to the nearest ten. Step 2 Change the divisor to a number that is compatible with 210. Notice it is easy to divide 210 by 7. Step 3 Divide mentally. So, is about = 30 DOGS Six dogs equally share a 45-pound bag of dog food each week. About how much does each dog eat each week? One Way: Use 45 and 5. Another Way: Use 48 and = = 8 So, each dog eats about 8 or 9 pounds of dog food each week. Estimate. Show your work. See Examples An contained 250 characters. The 4-line contained the same number of characters on each line. About how many characters were on each line? Show how you estimated. E 10. TALK MATH Explain how you could use compatible numbers to estimate Lesson 2A Divide Three- and Four-Digit Dividends 123

23 Estimate. t Show your work. See Examples Solve. Show your work. 27. A grocery store employee puts 8 bagels in each bag. If she has 385 bagels, about how many bags does she need? 28. Measurement Jani drives 240 miles in 4 hours. About how many miles does she drive each hour? 29. There were 317 marbles divided equally among 8 bowls. About how many marbles were in each bowl? 30. Measurement Emilio has 5 bags of birdseed. Each bag has about 28 ounces of birdseed. If he divides the birdseed equally into 3 containers, about how much birdseed will he put in each container? 31. The table shows how much each fifth grade room earned from a bake sale. The money is going to be given to 6 different charities. If each charity is given an equal amount, about how much will each charity receive? Show how you estimated. PRACTICE EXTRA Begins on page EP OPEN ENDED Write a division problem and show two different ways that you can estimate the quotient using compatible numbers. 33. NUMBER SENSE Without calculating, predict whether is greater than or less than 100. Explain your reasoning. 34. E WRITE MATH Write a real-life problem in which you estimate the quotient of two numbers. 124 Divide by a One-Digit Divisor

24 Test Practice 35. Which of the following is the most reasonable estimate for the number of Calories in one serving of milk? Servings of Milk Calories A. between 8 and 9 B. less than 80 C. between 80 and 90 D. more than A train traveled 300 miles in 5 hours. How far did the train travel each hour on average? F. 60 mi G. 150 mi H. 600 mi I. 1,500 mi 37. SHORT RESPONSE Mrs. Chong bought 480 bookmarks. If each box contains 60 bookmarks, how many boxes did she buy? Explain your reasoning. Solve. Use the guess, check, and revise strategy. (Lesson 1E) 38. Stacie counts 26 legs in a barnyard with horses and chickens. If there are 8 animals, how many are horses? Divide mentally. (Lesson 1D) , Divide. Use estimation to check. (Lesson 1C) 43. Miss Carbone read a book to her class. The book contained 54 pages and she read the same number of pages each day. If it took her 3 days to read the book, how many pages did she read each day? 44. BAR DIAGRAM Frankie paid $18 to rent a paddleboat. If the cost of renting is $6 per hour, for how many hours did Frankie rent the paddleboat? Divide. Use a related multiplication fact. (Lesson 1A) C04 005A A 48. Samuel swam a total of 48 laps over 4 days. He swam the same number of laps each day. How many laps did Samuel swim each day? (Lesson 1A) Lesson 2A Divide Three- and Four-Digit Dividends 125

25 Multi-Part Lesson 2 MP-Title Divide Three- and Four-Digit Dividends PART A B C D E F Main Idea I will explore division using models. Materials base-ten blocks Division Models with Greater Numbers You can also use base-ten blocks to divide greater numbers. At the fair, you need tickets to ride the rides. Three friends share 336 tickets equally. How many tickets will each friend receive? Find Step 1 Model 336 using base-ten blocks. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. Also addresses GLE Step 2 Divide the hundreds into 3 groups. Step 3 Divide the tens blocks into 3 groups. Step 4 Divide the ones blocks into 3 groups. So, = 112. Use multiplication to check your answer = Divide by a One-Digit Divisor

26 Model Remainders Find Step 1 Model 319 using base-ten blocks. Step 2 Divide the hundreds into 2 groups. Step 3 Divide the remaining ten and the ones into 2 groups. When you divide 319 into 2 groups, there are 159 in each group with one left over. So, = 159 R1. There is one left over. Use multiplication to check your answer = = 319 and Apply It Use models to find each quotient E WRITE MATH If you are dividing a three-digit even number by two, will you ever have a remainder? Explain. Lesson 2B Divide Three- and Four-Digit Dividends 127

27 Multi-Part Lesson 2 PART MP-Title Divide Three- and Four-Digit Dividends A B C D E F Main Idea I will divide using the distributive property and partial quotients. Distributive Property and Partial Quotients The Distributive Property allows you to divide each place-value position by the same factor. Vocabulary partial quotients Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. Jesse has 369 beads to be split evenly among 3 necklaces. How many beads can Jesse put on each necklace? Find using the Distributive Property and a bar diagram. Step 1 Model 369 as ( ) Step 2 Divide each section by 3. Write each quotient above the bar Step 3 Add the quotients = 123 So, = 123. Jesse can put 123 beads on each necklace. Check = Divide by a One-Digit Divisor

28 Partial quotients is a method of dividing where you break the dividend into sections that are easy to divide. Use Partial Quotients There are 738 students in Manuel s school. There are 6 grade levels in his school, with each grade having the same number of students. How many students are in the fifth grade? Find by using partial quotients. Step 1 Divide the hundreds. Since is 600, and 600 is close to 738, divide 600 by is a partial quotient. Subtract. Step 2 Divide the tens. Since 6 20 = 120, and 120 is close to 138, divide 120 by is a partial quotient. Subtract. Step 3 Divide the ones. There are only 18 left and 6 3 = is a partial quotient. Step 4 Add the partial quotients = 123 So, = 123. There are 123 students in the fifth grade. Check = and Apply It Divide. Use the Distributive Property Divide. Use partial quotients E WRITE MATH Suppose you are finding using partial quotients. Is 50 or 70 a more reasonable partial quotient? Explain. Lesson 2C Divide Three- and Four-Digit Dividends 129

29 Multi-Part Lesson PART 2 Divide Three- and Four-Digit Dividends A B C D E F Main Idea I will divide up to a four-digit number by a one-digit number. Get ConnectED Divide Three- and Four-Digit Dividends To divide a greater dividend by a one-digit divisor, use the same process as dividing a two-digit dividend by a one-digit divisor. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI Solve problems involving the division of twoand three-digit whole numbers by one- and two-digit whole numbers. RIDES In a 4-hour period, 852 people rode the Thunder Canyon ride. If the same number of people rode the ride each hour, how many people rode the ride in the first hour? Find Estimate = 225 Step 1 Divide the hundreds Divide: 8 4 Multiply: 2 4 Subtract: 8-8 Compare: 0 < 4 Step 3 Divide the ones Divide: 12 4 Multiply: 3 4 Subtract: Compare: 0 < 4 Step 2 Divide the tens Divide: 5 4 Multiply: 1 4 Subtract: 5-4 Compare: 1 < 4 So, 213 people rode Thunder Canyon in the first hour. Check = Divide by a One-Digit Divisor

30 Divide by a One-Digit Number Find Estimate = 450 Step 1 Divide the hundreds < 2 Step 2 Divide the tens < 2 Step 3 Divide the ones < 2 The quotient is 428. Compare to the estimate. Divide a Four-Digit Number Find 7, Step 1 Divide the thousands. Step 2 Divide the hundreds , , < < 6 To check division with a remainder, first multiply the quotient and the divisor. Then add the remainder. 1, ,944 7, ,946 Step 3 Divide the tens , < 6 The quotient is 1,324 R2. Step 4 Divide the ones. 1,324 R2 6 7, < 6 Lesson 2D Divide Three- and Four-Digit Dividends 131

31 Divide. See Examples , , Three adult kangaroos weigh 435 pounds. If each adult weighs the same, how much would one adult kangaroo weigh? E 10. TALK MATH Does the quotient of 945 and 8 have two or three digits? Explain how you know without solving. Divide. iid See Examples , PRACTICE EXTRA Begins on page EP , , BAR DIAGRAM A state park has cable cars that travel about 864 yards in 4 minutes. How many yards do the cars travel per minute? 28. Three new video game systems cost $645. If all the game systems cost the same, what is the cost of each game system? 1 min 1 min 1 min 1 min? yd 864 yards 29. On Monday, a concession stand manager ordered 985 popcorn bags. She splits the bags evenly among 5 concession stands. How many popcorn bags will each concession stand receive? 30. Mr. Harris wants to divide his 36 students into equal groups of 3 students each. How many groups of 3 students can he make? How many students will not be in a group of 3? 132 Divide by a One-Digit Divisor

32 31. OPEN ENDED Write a real-world division problem with a divisor of 4 that has no remainder. Then write a real-world division problem with a divisor of 4 that has a remainder. 32. NUMBER SENSE Place the digits 2, 4, 7, and 8 in to create a division problem with the greatest quotient. 33. E WRITE MATH Explain how estimation is useful when solving division problems. Test Practice 34. Use the table below to make a true statement. Weight of Whales Mammal Weight Blue whale 144 tons Gray whale 36 tons 35. Lauren poured an equal amount of the solution below in each of 4 test tubes. How much solution is in each test tube? A blue whale is about heavier than a gray whale. A. 3 times C. 6 times F. 30 ml H. 105 ml B. 4 times D. 8 times G. 100 ml I. 110 ml Divide. Use the partial quotients method. (Lesson 2C) Enrique has 685 trading cards that he wants to place into 5 different albums. If each album will hold the same number of cards, how many cards will fit in each album? (Lesson 2C) 39. There are 520 baseballs that will be shipped to nine sports stores. Estimate the number of baseballs each store is to receive if they each receive about the same number. (Lesson 2A) Divide. Use a related multiplication fact. (Lesson 1A) Lesson 2D Divide Three- and Four-Digit Dividends 133

33 Multi-Part Lesson PART 2 Divide Three- and Four-Digit Dividends A B C D E F Main Idea I will understand how to place the first digit in a quotient. Get ConnectED Place the First Digit Sometimes you may have a three-digit dividend, but there are not enough hundreds to divide. If so, the quotient should start at the next place value position. GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Solve problems involving the division of twoand three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE Raven received 135 s over 3 weeks. If she received the same number of s each week, how many s did she receive in the first week? Find Step 1 Divide the hundreds There are not enough hundreds to divide into three groups. So, regroup the hundreds block into 10 tens. Step 2 Divide the tens. 4 The first digit of the quotient is in - 12 the tens place. 15 Step 3 Divide the ones So, = 45. Raven received 45 s in the first week. Check 45 3 = Divide by a One-Digit Divisor

34 Divide Find Estimate = 100 Step 1 Step 2 Step 3 First estimate your answer by rounding or using compatible numbers = 100 So, is about 100. Divide the hundreds Since 7 > 6, look at the tens. 7 < 68. The first digit is in the tens place. Divide the tens Divide the ones. 97 R So, = 97 R5. Compare to the estimate. 97 R5 100 The symbol means about or almost equal to. Divide. Check your answer using multiplication. See Examples 1 and R There are 594 people standing in line to see a movie premiere. The movie is playing in 6 theaters. If the same number of people will see the movie in each theater, how many people will be in one theater? E 13. TALK MATH If the first digit in the dividend is less than the number in the divisor, where will you begin writing your quotient? Lesson 2E Divide Three- and Four-Digit Dividends 135

35 Divide. iid Check your answer using multiplication. lili i See Examples 1 and R There are 624 envelopes to be sorted into 8 different mail bags. If the same number of envelopes will be in each bag, how many envelopes will be in one bag? Use the information to solve the problem. PRACTICE EXTRA Begins on page EP How much food does one manatee eat in a day if the three manatees eat the same amount? 31. WHICH ONE DOESN T BELONG? Identify the expression that does not have a two-digit quotient E WRITE MATH Can you determine the number of digits in the quotient of without dividing? Explain. 136 Divide by a One-Digit Divisor

36 C01-031A Multi-Part Lesson 2 PART Divide Three- and Four-Digit Dividends A B C D E F Main Idea I will solve division problems that result in quotients that have zeros. Quotients with Zeros Sometimes quotients will contain zeros. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. GLE Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals. SPI Solve problems involving the division of twoand three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE ELECTRONICS Maya is saving to buy a television. The television costs $327. She plans to save money for 3 months. How much does Maya need to save each month to buy the television? Find $ Estimate = 100 Step 1 Divide the hundreds Step 2 Divide the tens. $ Notice there are not enough tens to divide. Place a 0 in the quotient. Step 3 Divide the ones Regroup the two tens as twenty ones. There are now 27 ones. Maya needs to save $109 each month. Compare to the estimate. $109 $100. Lesson 2F Divide Three- and Four-Digit Dividends 137

37 Quotients with Zeros Use the same strategy to divide a three-digit number that you used to divide a two-digit number. Find Estimate = 125 Step 1 Divide the hundreds Step 2 Divide the tens Step 3 Divide the ones So, = 130 R3. There are not enough ones to divide. Place 0 in the ones place. The remainder is 3. Compare 130 R3 to the estimate. 130 R3 125 Check using multiplication = 520, = 523 Divide. See Examples 1 and , , BAR DIAGRAM There are 630 minutes of music to be put on 6 CDs. If the same number of minutes fit on each CD, how many minutes of music fit on each CD? E 11. TALK MATH Explain how to model finding the quotient using base-ten blocks. 138 Divide by a One-Digit Divisor

38 Divide. id See Examples 1 and PRACTICE EXTRA Begins on page EP , , There are 312 fish at the aquarium in 3 different fish tanks. Each tank has the same number of fish. How many fish are in each tank? Use the information to solve the problem. 25. Kirk has watched 120 minutes of television in the last 4 days. He watched the same amount of television each day. How many minutes of television did he watch in 1 day? 26. How much does one manatee eat if the three manatees eat the same amount? 27. OPEN ENDED Write two division problems that have zeros in the quotient. One of the problems should have a remainder and the other should not. 28. WHICH ONE DOESN T BELONG? Identify the division problem that does not belong with the other three. Explain NUMBER SENSE In problems like 714 7, where the digit in the greatest place of the dividend is the same as the divisor, will the quotient always have a zero? If not, give an example. 30. E WRITE MATH Explain how to find the quotient of To assess partial mastery of SPI , see your Tennessee Assessment Book. 139

39 Multi-Part Lesson 3 Interpret the Remainder PART A B C D E Interpret the Remainder Main Idea I will explore interpreting the remainder in a division problem. Materials connecting cubes Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI Recognize the unit associated with the remainder in a division problem or the meaning of the fractional part of a whole given in either decimal or fraction form. SPI Select a reasonable solution to a real-world division problem in which the remainder must be considered. Also addresses GLE , GLE The following activities show you how to use remainders in different kinds of problems. A group of fifth graders collected 46 cans of food to donate to 3 food banks. If each food bank is to get an equal number of cans, how many cans do they each receive? Step 1 Use 46 connecting cubes to represent the cans of food. Use three paper plates to represent the food banks. Divide the cubes equally among the three plates. Step 2 Interpret the remainder. Since each food bank is to get the same number of cans of food, they will each receive 15 cans. There is one can left over. 140 Divide by a One-Digit it Divisori

40 A total of 35 students are going on a field trip to NASA s Johnson Space Center in Houston. If there needs to be an adult for every 8 students, how many adults are needed? Use 35 connecting cubes to represent the students. Use paper plates to represent the adults. Place 8 cubes on as many plates as possible. Place any leftover cubes on a plate. Interpret the remainder. There are 4 groups of 8 students. They will each need an adult. There are 3 students who are not enough for a full group of 8. They will also need an adult. So, or 5 adults are needed. About It 1. In Activity 1, the remainder was dropped. Explain why. 2. In Activity 2, the quotient was rounded up to 5. Explain why. and Apply It State the solution and explain how to interpret the remainder in each division problem. 3. Each picnic table at a park seats 6 people. How many tables will 83 people at a family reunion need? 4. Mrs. Malone has $150 to buy volleyballs for Lincoln Middle School. How many can she buy at $9 each? 5. E WRITE MATH Suppose 2 friends want to share 5 cookies evenly. Interpret the remainder in two different ways. Lesson 3A Interpret the Remainder 141

41 Multi-Part Lesson 3 PART Interpret the Remainder A B C D E Main Idea I will interpret the remainder in a division problem. Interpret the Remainder It is important to know what the remainder represents. In some situations, the remainder may require you to increase the quotient. Get ConnectED GLE Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division. SPI Select a reasonable solution to a realworld division problem in which the remainder must be considered. SPI Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers. Also addresses GLE , SPI TREES A state park has 257 evergreens to plant equally in 9 areas. How many evergreens are planted in each area? What does the remainder represent? Step 1 Divide. 28 R Step 2 Interpret the remainder, 5. The remainder, 5, means there are 5 evergreens left over after 28 are planted in each of the 9 areas. So, the park plants 28 evergreens in each area and 5 evergreens are left. PARTY There are 174 guests invited to a dinner. Each table seats 8 guests. How many tables are needed? Step 1 Divide. 21 R Step 2 Interpret the remainder, 6. There are 6 guests left over, which is not enough for a full table of 8. But, they also need a table. So, a total of , or 22 tables are needed. 142 Divide by a One-Digit Divisor

42 6A Solve. Explain how you interpreted the remainder. See Examples 1 and 2 1. A tent is put up with 7 poles. How many tents can be put up with 200 poles? 2. There are 50 students traveling in vans on a field trip. Each van seats 8 students. How many vans are needed? 3. How many payments of $10 would it take Samuel to purchase the scooter shown at the right? 4. E TALK MATH Discuss the different ways you C04-016A can interpret the remainder in a division problem. Solve. Explain how you interpreted t the remainder. See Examples 1 and 2 5. Mrs. Hodges made 144 muffins for a bake sale. She puts them into tins of 5 muffins each. How many tins of muffins can she make? 6. Students on the softball team earned $295 from a carwash. How many team banners shown can they buy? PRACTICE EXTRA Begins on page EP2. 7. Measurement How many 8-foot sections of fencing are needed for 189 feet of fence? $ Valerie has 20 stuffed animals. She wants to store them in plastic bags. She estimates she can fit three stuffed animals in each bag. How many bags will she need? 9. Mrs. Flores is buying scrapbooks for her store. Her budget is $350. How many of the scrapbooks shown can she buy? SCRAPBOOK 10. Measurement How many 6-ounce cups can be filled from 4 gallons of juice? (Hint: 1 gallon = 128 ounces) 11. Measurement Water stations will be placed every 400 meters of a 5-kilometer race. How many water stations are needed? (Hint: 1 kilometer = 1,000 meters) 12. BAR DIAGRAM Three yards of fabric will be cut into pieces so that each piece is 8 inches long. How many pieces can be cut? (Hint: 1 yard = 36 inches) Lesson 3B Interpret the Remainder 143

43 Food Six friends decide to pack and share an extra large submarine sandwich, which is cut into 20 equal size pieces. The cost of the submarine sandwich is $21, not including tax. 13. How much would each friend pay if each one paid the same amount? Explain how you interpreted the remainder. 14. How many pieces would each friend receive if each one receives the same amount? Explain how you interpreted the remainder. 15. Three pieces will fit into one plastic bag. How many plastic bags are needed to pack the 20 pieces? Explain how you interpreted the remainder. 16. OPEN ENDED Write a real-world situation that could be described by the division problem 38 5 = 7 R3 in which it makes sense to round the quotient up to CHALLENGE If the divisor is 30, what is the least three-digit dividend that would give a remainder of 8? Explain. CHALLENGE Consider each situation. In each case, decide whether you would drop the remainder, round the quotient up, or represent the quotient as a fraction or decimal to solve each problem. Explain your reasoning. Then solve each problem. 18. Ernesto spent $50 on four identical photo frames. How much did he spend on each frame? 19. Two friends share 3 cookies equally. How many cookies did each friend get? 20. Measurement A piece of string 50 inches long will be cut into pieces so that each piece is 4 inches long. How many full-length pieces can be cut from the string? 21. E WRITE MATH Write a real-world division problem that can be solved by interpreting the remainder. Does it make sense to round up or down to the next whole number? Explain. 144 Divide by a One-Digit Divisor

44 Test Practice 22. Forty-six students are visiting a dinosaur exhibit. A tour guide is needed for each group of 6 students. How many tour guides are needed? A. 7 B. 8 C. 40 D Ms. Meir wants to divide 135 maps as equally as possible among 4 zoo guides. Which is a true statement? F. All 4 guides will get 34 maps. G. Three guides will get 33 maps and 1 guide will get 34 maps. H. Three guides will get 34 maps and 1 guide will get 33 maps. I. Two guides will get 33 maps and 2 guides will get 34 maps. Divide. (Lesson 2F) Estimate. Show your work. (Lesson 2A) A penguin swam at 9 miles per hour. About how many hours would it take for the penguin to travel 362 miles? Solve. Use the guess, check, and revise strategy. 32. BAR DIAGRAM The teacher asked three students to bring in cereal boxes for an art project. Dwayne brought in 3 less than Mandy. Mandy had twice as many as Steve. How many boxes did each student bring, if there were a total of 22 boxes? (Lesson 1E) Divide mentally. (Lesson 1D) , Jack owed $240 for a drum set that he needed to pay off in 6 months. How much will Jack need to pay each month in order to pay for the drum set on time? Lesson 3B Interpret the Remainder 145