5th Grade. Division.

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1 1

2 5th Grade Division

3 Division Unit Topics Click on the topic to go to that section Divisibility Rules Patterns in Multiplication and Division Division of Whole Numbers Division of Decimals Glossary & Standards Teacher Notes 3

4 Divisibility Rules Return to Table of Contents 4

5 Divisible Divisible is when one number is divided by another, and the result is an exact whole number. five three Example: 15 is divisible by 3 because 15 3 = 5 exactly. 5

6 Divisible two four BUT, 9 is not divisible by 2 because 9 2 is 4 with one left over. 6

7 Divisibility A number is divisible by another number when the remainder is 0. There are rules to tell if a number is divisible by certain other numbers. 7

8 Divisibility Rules Look at the last digit in the Ones Place! 2 Last digit is even 0,2,4,6 or 8 5 Last digit is 5 OR 0 10 Last digit is 0 Check the Sum! 3 Sum of digits is divisible by 3 6 Number is divisible by 3 AND 2 9 Sum of digits is divisible by 9 Look at Last Digits 4 Last 2 digits form a number divisible by 4 8

9 Divisibility Rules Click for Link Divisibility Rules You Tube song 9

10 Divisibility Practice Let's Practice! Is 34 divisible by 2? Yes, because the digit in the ones place is an even number. 34 / 2 = 17 Is 1,075 divisible by 5? Yes, because the digit in the ones place is a 5. 1,075 / 5 = 215 Is 740 divisible by 10? Yes, because the digit in the ones place is a / 10 = 74 10

11 Divisibility Practice Is 258 divisible by 3? Yes, because the sum of its digits is divisible by = 15 Look 15 / 3 = / 3 = 86 Is 192 divisible by 6? Yes, because the sum of its digits is divisible by 3 AND = 12 Look 12 /3 = / 6 = 32 11

12 Divisibility Practice Is 6,237 divisible by 9? Yes, because the sum of its digits is divisible by = 18 Look 18 / 9 = 2 6,237 /9 = 693 Is 520 divisible by 4? Yes, because the number made by the last two digits is divisible by / 4 = / 4 =

13 1 Is 198 divisible by 2? Yes No 13

14 2 Is 315 divisible by 5? Yes No 14

15 3 Is 483 divisible by 3? Yes No 15

16 4 294 is divisible by 6. True False 16

17 5 3,926 is divisible by 9. True False 17

18 Divisibility Some numbers are divisible by more than 1 digit. Let's practice using the divisibility rules. 18 is divisible by how many digits? Let's see if your choices are correct. 9 Click Did you guess 2, 3, 6 and 9? 165 is divisible by how many digits? Let's see if your choices are correct. Click Did you guess 3 and 5?

19 Divisibility 28 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2 and Click 4? 530 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2, 5, Click and 10? Now it's your turn... 19

20 Divisibility Table Complete the table using the Divisibility Rules. (Click on the cell to reveal the answer) Divisible by2 by 3 by 4 by 5 by 6 by 9 by ,218 1,006 28,550 20

21 6 What are all the digits 15 is divisible by? 21

22 7 What are all the digits 36 is divisible by? 22

23 8 What are all the digits 1,422 is divisible by? 23

24 9 What are all the digits 240 is divisible by? 24

25 10 What are all the digits 64 is divisible by? 25

26 Patterns in Multiplication and Division Return to Table of Contents 26

27 Number Systems A number system is a systematic way of counting numbers. For example, the Myan number system used a symbol for zero, a dot for one or twenty, and a bar for five. 27

28 Number Systems There are many different number systems that have been used throughout history, and are still used in different parts of the world today. Sumerian wedge = 10, line = 1 Roman Numerals 28

29 Our Number System Generally, we have 10 fingers and 10 toes. This makes it very easy to count to ten. Many historians believe that this is where our number system came from. Base ten. 29

30 Base Ten We have a base ten number system. This means that in a multidigit number, a digit in one place is ten times as much as the place to its right. Also, a digit in one place is 1/10 the value of the place to its left. 30

31 Base 10 How do you think things would be different if we had six fingers on each hand? 31

32 Powers of 10 Numbers can be VERY long. $100,000,000,000,000 Wouldn't you love to have one hundred trillion dollars? Fortunately, our base ten number system has a way to make multiples of ten easier to work with. It is called Powers of

33 Powers of 10 Numbers like 10, 100 and 1,000 are called powers of 10. They are numbers that can be written as products of tens. 100 can be written as 10 x 10 or ,000 can be written as 10 x 10 x 10 or

34 Powers of The raised digit is called the exponent. The exponent tells how many tens are multiplied. 34

35 Powers of 10 A number written with an exponent, like 10 3, is in exponential notation. A number written in a more familiar way, like 1,000 is in standard notation. 35

36 Powers of 10 Powers of 10 (greater than 1) Standard Product Exponential Notation of 10s Notation x , x 10 x , x 10 x 10 x , x 10 x 10 x 10 x ,000, x 10 x 10 x 10 x 10 x

37 Powers of 10 Remember, in powers of ten like 10, 100 and 1,000 the zeros are placeholders. Each place holder represents a value ten times greater than the place to its right. Because of this, it is easy to MULTIPLY a whole number by a power of

38 Multiplying Powers of 10 To multiply by powers of ten, keep the placeholders by adding on as many 0s as appear in the power of 10. Examples: 28 x 10 = 280 Add on one 0 to show 28 tens 28 x 100 = 2,800 Add on two 0s to show 28 hundreds 28 x 1,000 = 28,000 Add on three 0s to show 28 thousands 38

39 Multiplying Powers of 10 If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10. Steps 50 x 100 = 5, Multiply the digits to the left of the zeros in each factor. 50 x x 1 = 5 2. Count the number of zeros in each factor. 50 x Write the same number of zeros in the product. 5, x 100 = 5,000 39

40 Multiplying Powers of x 400 = steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = Count the number of zeros in each factor. 3. Write the same number of zeros in the product. 40

41 60 x 400 = Multiplying Powers of 10 steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = Count the number of zeros in each factor. 60 x Write the same number of zeros in the product. 41

42 60 x 400 = Multiplying Powers of 10 steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = Count the number of zeros in each factor. 60 x Write the same number of zeros in the product. 60 x 400 = 24,000 42

43 Multiplying Powers of x 70,000 = steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = Count the number of zeros in each factor. 3. Write the same number of zeros in the product. 43

44 Multiplying Powers of x 70,000 = steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = Count the number of zeros in each factor. 500 x 70, Write the same number of zeros in the product. 44

45 Multiplying Powers of x 70,000 = steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = Count the number of zeros in each factor. 500 x 70, Write the same number of zeros in the product. 500 x 70,000 = 35,000,000 45

46 Practice Finding Rule Your Turn... Write a rule. Input Output 50 15, , , ,000 click Rule multiply by

47 Practice Finding Rule Write a rule. Input Output 20 18, ,300 9,000 8,100,000 Rule clickmultiply by ,000 47

48 11 30 x 10 = 48

49 x 1,000 = 49

50 x 10,000 = 50

51 x 5,100 = 51

52 15 70 x 8,000 = 52

53 16 40 x 500 = 53

54 17 1,200 x 3,000 = 54

55 18 35 x 1,000 = 55

56 Dividing Powers of 10 Because of this, it is easy to DIVIDE a whole number by a power of 10. Remember, a digit in one place is 1/10 the value of the place to its left. Take off as many 0s as appear in the power of 10. Example: 42,000 / 10 = 4,200 Take off one 0 to show that it is 1/10 of the value. 42,000 / 100 = 420 Take off two 0's to show that it is 1/100 of the value. 42,000 / 1,000 = 42 Take off three 0's to show that it is 1/1,000 of the value. 56

57 Dividing Powers of 10 If you have memorized the basic division facts, you can solve problems mentally. Use a pattern when dividing by powers of / 10 = 60 / 10 = 6 steps 1. Cross out the same number of 0's in the dividend as in the divisor. 2. Complete the division fact. 57

58 Practice Dividing More Examples: 700 / / 10 = 70 8,000 / 10 8,000 / 10 = 800 9,000 / 100 9,000 / 100 = 90 58

59 120 / / 30 = 4 Practice Dividing This pattern can be used in other problems. 1,400 / 700 1,400 / 700 = 2 44,600 / ,600 / 200 =

60 Practice Dividing Rule Your Turn... Complete. Follow the rule. Rule: Divide by 50 Input ,000 Output click click click

61 Practice Dividing Rule Complete. Find the rule. Find the rule. Input Output click click 2, click 61

62 / 10 = 62

63 20 16,000 / 100 = 63

64 21 1,640 / 10 = 64

65 / 30 = 65

66 23 80 / 40 = 66

67 / 80 = 67

68 25 4,500 / 50 = 68

69 Powers of 10 Remember Powers of 10 (greater than 1) Let's look at Powers of 10 (less than 1) Powers of 10 (less than 1) Standard Notation Product of 0.1 Exponential Notation x x 0.1 x x 0.1 x 0.1 x x 0.1 x 0.1 x 0.1 x x 0.1 x 0.1 x 0.1 x 0.1 x

70 Powers of 10 What if the exponent is zero? (10 0 ) The number 1 is also called a Power of 10, because 1 = ,000s 1,000s 100s 10s 1s 0.1s 0.01s 0.001s s Each exponent is 1 less than the exponent in the place to its left. This is why mathematicians defined 10 0 to be equal to 1. 70

71 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Example: 1,000 x 45.6 =? Steps 1. Locate the decimal point in the power of 10. 1,000 = 1, Move the decimal point LEFT until you get to the number Move the decimal point in the other factor (3 places) the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer So, 1,000 x 45.6 = 45,000 71

72 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Steps Example: 1,000 x 45.6 =? 1. Locate the decimal point in the power of 10. 1,000 = 1, Move the decimal point LEFT until you get to the number Move the decimal point in the other factor (3 places) the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer So, 1,000 x 45.6 = 45,000 72

73 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Steps Example: 1,000 x 45.6 =? 1. Locate the decimal point in the power of 10. 1,000 = 1, Move the decimal point LEFT until you get to the number Move the decimal point in the other factor (3 places) the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer So, 1,000 x 45.6 = 45,000 73

74 Let's try some together. Practice Multiplying 10,000 x 0.28 = $4.50 x 1,000 = 1.04 x 10 = 74

75 x 3.67 = 75

76 x 10,000 = 76

77 28 1,000 x $8.98 = 77

78 x 10 = 78

79 Dividing Powers of 10 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the 1,000 = 1,000. power of Move the decimal point LEFT until you get (3 places) to the number Move the decimal point in the other number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 =

80 Dividing Powers of 10 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the 1,000 = 1,000. power of Move the decimal point LEFT until you get (3 places) to the number Move the decimal point in the other number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 =

81 Dividing Powers of 10 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the 1,000 = 1,000. power of Move the decimal point LEFT until you get (3 places) to the number Move the decimal point in the other number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 =

82 Let's try some together. Practice Dividing 56.7 / 10 = 0.47 / 100 = $290 / 1,000 = 82

83 / 10 = 83

84 / 100 = 84

85 32 $456 / 1,000 = 85

86 33 60 / 10,000 = 86

87 34 $89 / 10 = 87

88 / 100 = 88

89 Division of Whole Numbers Return to Table of Contents 89

90 Review from 4th Grade When you divide, you are breaking a number apart into equal groups. The problem 15 3 means that you are making 3 equal groups out of 15 total items. Each equal group contains 5 items, so 15 3 = 5 90

91 Review from 4th Grade How will knowing your multiplication facts really well help you to divide numbers? click to reveal Multiplying is the opposite (inverse) of dividing, so you're just multiplying backwards! Find each quotient. (You may want to draw a picture and circle equal groups!) click click click click 91

92 Review from 4th Grade You will not be able to solve every division problem mentally. A problem like 56 4 is more difficult to solve, but knowing your multiplication facts will help you to find this quotient, too! To make this problem easier to solve, we can use the same Area Model that we used for multiplication. How can you divide 56 into two numbers that are each divisible by 4? (? +? = 56) 4?? 56 92

93 Review from 4th Grade You can break 56 into and then divide each part by 4.?? Ask yourself... What is 40 4? What is 16 4? (or 4 x n = 40?) (or 4 x n = 16?) The quotient of 56 4 is equal to the sum of the two partial quotients. 93

94 Area Model Division Let's try another example. Use the area model to find the quotient of How can you break up 135? Remember... you want the numbers to be divisible by

95 Area Model Division Let's try another example. Use the area model to find the quotient of You can break 135 into and then divide each part by 15.?? Ask yourself... What is 90 15? What is 45 15? (or 15 x n = 90?) (or 15 x n = 45?) The quotient of is equal to the sum of the two partial quotients. 95

96 Area Model Division What about remainders? Use the area model to find the quotient =?? R

97 36 Use the area model to find the quotient = 97

98 37 Use the area model to find the quotient. Write any reminder as a fraction = 98

99 38 Use the area model to find the quotient. Write any reminder as a fraction = 99

100 39 A teacher drew an area model to find the value of 6, Determine the number that each letter in the model represents and explain each of your answers. Write the quotient and remainder for Explain how to use multiplication to check that the quotient is correct. You may show your work in your explanation. From PARCC PBA sample test #15 100

101 Division Key Terms Some division terms to remember... The number to be divided into is known as the dividend. The number which divides the dividend is known as the divisor. The answer to a division problem is called the quotient. divisor 5 4 quotient 20 dividend 20 5 = = 4 101

102 Estimating Estimating the quotient helps to break whole numbers into groups. 102

103 Estimating: One Digit Divisor 8) ) )689 Divide 8) 68 Write 0 in remaining place. 80 is the estimate. 103

104 One Digit Estimation Practice Estimate: 9)507 Remember to divide 50 by 9 Then write 0 in remaining place in quotient. Is your estimate 50 or 40? Click Yes, it is

105 One Digit Estimation Practice Estimate : 5)451 Remember to divide 45 by 5 Then write 0 in remaining place in quotient. Is your estimate 90 or 80? Click Yes, it is

106 40 The estimation for 8)241 is 40? True False 106

107 41 Estimate

108 42 Estimate 4)

109 43 Solve using Estimation. Marta baby sat fo r four hours and earned $19. ABOUT how much money did Marta earn each hour that she baby sat? 109

110 Estimating: Two Digit Divisor 26)6,498 30)6,498 Round 26 to its greatest place. 2 30) 6,498 Divide 30) Write 0 in remaining places. 30)6, is the estimate. 110

111 Two Digit Estimation Practice Estimate: 31)637 Remember to round 31 to its greatest place 30, then divided 63 by 30. Finally, write 0's in remaining places in quotient. Is your estimate 20 or 30? click to reveal Yes, it is

112 Estimate: Two Digit Estimation Practice 87)9,321 Remember to round 87 to its greatest place 90, then divide 93 by 90 Finally, write 0's in remaining places in quotient. Is your estimate 100 or 1,000? click to reveal Yes, it is

113 44 The estimation for 17)489 is 2? True False 113

114 45 Estimate 5,

115 46 Estimate 41) 2,

116 47 Estimate 31)7,

117 48 Solve using Estimation. Brandon bought cookies to pack in his lunch. He bought a box with 28 cookies. If he packs five cookies in his lunch each day, ABOUT how many days will the days will the cookies last? 117

118 Division When we are dividing, we are breaking apart into equal groups. Find Step 1: Can 3 go into 1, no so can Click for step 1 3 go into 13, yes Step 2: Bring down the 2. Can 3 Click for step 2 go into 12, yes x 4 = = 1 Compare 1 < 3 3 x 4 = = 0 Compare 0 < 3 118

119 Division Step 3: Check your answer. 44 x

120 49 Divide and Check 8)

121 50 Divide and Check 9)

122 51 Divide and Check

123 52 Divide and Check

124 53 Adam has a wire that is 434 inches long. He cuts the wire into 7 inch lengths. How many pieces of wire will he have? 124

125 54 Bill and 8 friends each sold the same number of tickets. They sold 117 tickets in all. How many tickets were sold by each person? 125

126 55 There are 6 outs in an inning. How many innings would have to be played to get 348 outs? 126

127 56 How many numbers between 23 and 41 have NO remainder when divided by 3? A 4 B 5 C 6 D

128 Division Problem John and Lad are splitting the $9 that John has in his wallet. Move the money to give John half and Lad half. Sometimes, when we split a whole number into equal groups, there will be an amount left over. The left over number Click when is called finished. the remainder. 128

129 Long Division Lets look at remainders with long division. For example: 4 7) We say there are 2 left over, because you can not make a group of 7 out of

130 Long Division For example: 4 7) = 4 R This is the way you may have seen it. The R stands for remainder. 130

131 Long Division Another example: 23 15) We say there are 13 left over (R) because you can not make a group of 15 out of = 23 R

132 57 A group of six friends have 83 pretzels. If they want to share them evenly, how many will be left over? 132

133 58 Four teachers want to evenly share 245 pencils. How many will be left over? 133

134 59 Twenty students want to share 48 slices of pizza. How many slices will be left over, if each person gets the same number of slices? 134

135 60 Suppose there are 890 packages being delivered by 6 planes. Each plane is to take the same number of packages and as many as possible. How many packages will each plane take? How many will be left over? Fill in the blanks. Each plane will take packages. There will be packages left over. A B 149 packages, 2 left over 148 packages, 2 left over 135

136 Long Division Instead of writing an R for remainder, we will write it as a fraction of the 30 that will not fit into a group of 7. So 2/7 is the remainder. 4 7)

137 Long Division Examples More examples of the remainder written as a fraction: 7 6) The Remainder means that there is 5 left over that can't be put in a group containing 6 To Check the answer, use multiplication and addition. 7 x = = 47 Multiply the quotient and the divisor. Then, add the remainder. The result should be the dividend. 137

138 Long Division Example Example: 37 7) Check the answer using multiplication and addition.way 1: 37 x = = 264 Way 2: 37 quotient x 7 x divisor remainder 264 dividend 138

139 61 Divide and Check 4)43 (Put answer in as a mixed number.) 139

140 62 Divide and Check 61 3 = (Put answer in as a mixed number.) 140

141 63 Divide and Check (Put answer in as a mixed number.) 141

142 64 Divide and Check 2)811 (Put answer in as a mixed number.) 142

143 65 Divide and Check = (Put answer in as a mixed number.) 143

144 Long Division with 2 digit Divisor You can divide by two digit divisors to find out how many groups there are or how many are in each group. When dividing by a two digit divisor, follow the steps you used to divide by a one digit divisor. Repeat until you have divided all the digits of the dividend by the divisor. STEPS Divide Multiply Subtract Compare Bring down next number 144

145 Long Division Practice Find Step 1: Can 25 go into 4, no so can 25 go into 45, yes Step 2: Bring down Click for the step 7. Can 2 25 go into 207, yes x 1 = = 20 Compare 20 < x 8 = = 7 Compare 7 < 25 Step 3: Bring down the 5. Can Click for step 3 25 go into 75, yes 25 x 3 = = 0 Click for step 1 Compare 0 <

146 Step 3: Check your answer. Long Division Practice 183 x

147 Long Division Example Mr. Taylor's students take turns working shifts at the school store. If there are 23 students in his class and they work 253 shifts during the year, how many shifts will each student in the class work? 147

148 Long Division Example 23)253 Step 1 Compare the divisor to the dividend to decide where to place the first digit in the quotient. Divide the tens. Think: What number multiplies by 23 is less than or equal to 25. Step 2 Multiply the number of tens in the quotient times the divisor. Subtract the product from the dividend. Bring down the next number in the dividend. Step 3 Divide the result by 23. Write the number in the ones place of the quotient. Think: What number multiplied by 23 is less than or equal to 23? Step 4 Multiply the number in the ones place of the quotient by the divisor. Subtract the product from 23. If the difference is zero, there is no remainder ) Each student will work 11 shifts at the school store. 148

149 Long Division Division Steps can be remembered using a "Silly" Sentence. David Makes Snake Cookies By Dinner. Divide Multiply Subtract Compare Bring Down What is your "Silly" Sentence to remember the Division Steps? 149

150 Silly Steps Example Click boxes to show work Find Step 1 22) 374 Step ) x 22 Step Think 20) 374 divide multiply 22) subtract less than 22 compare Step 4 1 bring down 22) bring down Step 5 17 repeat 22) repeat Final Step 17 x 22 Check

151 66 A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds of chocolate does the factory produce in 1 hour? A 38 B 40 C 41 D

152 67 Teresa got a loan of $7,680 for a used car. She has to make 24 equal payments. How much will each payment be? A $230 B $320 C $

153 68 Solve 16)

154 69 Solve

155 70 If 280 chairs are arranged into 35 rows, how many chairs are in each row? 155

156 71 There are 52 snakes. There are 13 cages. If each cage contains the same number of snakes, how many snakes are in each cage? 156

157 72 Solve 46)3,

158 73 Solve 3,

159 74 Enter your answer. 1, = From PARCC EOY sample test #27 159

160 Division Steps When dividing by a Two Digit Divisor, there may be a Remainder. Follow the Division Steps. Divide Multiply Subtract Compare Bring Down Repeat. If the Difference in the Last Step of Division is not a Zero, and there are no other numbers to Bring Down, this is the Remainder. The definition of a Remainder is an amount "left over" that does not make a full group (Divisor). Write the Remainder as a Fraction. top number Difference 62 bottom number Divisor 77 This means there are 62 "left over" that do not make a full group of 77. Use Multiplication and Addition to check you. Problem: ) x = 447 OR 77 x

161 Let's Practice Remember your Steps: Divide, Multiply, Subtract, Compare, Bring Down, Write the Remainder as a Fraction, Check your work ) Solve CHECK 36 x Divisor x Quotient + Remainder = Dividend 161

162 75 What is the remainder when 402 is divided by 56? A 8 B 7 C 19 D

163 76 What is the remainder when 993 is divided by 38? A 5 B 8 C 13 D

164 77 Divide 80) 104 (Put answer in as a mixed number.) 164

165 78 Divide (Put answer in as a mixed number.) 165

166 79 Divide 45) 1442 (Put answer in as a mixed number.) 166

167 80 Divide (Put answer in as a mixed number.) 167

168 81 Divide 83) 8537 (Put answer in as a mixed number.) 168

169 Interpreting the Remainder In word problems, we need to interpret the what the remainder means. For example: Celina has 58 pencils and wants to share them with 5 people. 11 5) people will each get 11 pencils, and there will be 3 left over. 169

170 Interpreting the Remainder What does the remainder below mean? Violet is packing books. She has 246 books and, 24 fit in a box. How many boxes does she need? 10 24) The remainder means she would have 6 books that would not fit in the 10 boxes. She would need 11 boxes to fit all the books. 170

171 82 If you have 341 oranges to transport from Florida to New Jersey, and 7 oranges are in each bag, how many bags will you need to ship all of the oranges? A 47 B 48 C 49 D

172 83 At the bakery, donuts are only sold in boxes of 12. If 80 donuts are needed for the teacher's meeting, how many boxes should be bought? A 6 B 7 C 8 D 9 172

173 84 Apples cost $4 for a 5 pound bag. If you have $19, how many bags can you buy? A = 4 R 3 B 3 C 4 D 5 173

174 85 The school is ordering carry cases for the calculators. If there are 203 calculators and 16 fit in a case, how many cases need to be ordered? A 10 B 11 C 12 D

175 86 For the class trip, 51 people fit on a bus and 267 people are going. How many buses will be needed? A 5 B 6 C 7 D 8 175

176 87 Greg is volunteering at a track meet. He is in charge of providing the bottled water. Greg knows these facts. The track meet will last 3 days. There will be 117 athletes, 7 coaches, and 4 judges attending the track meet. Once case of bottled water contains 24 bottles. The table shows the number of bottles of water each athlete coach, and judge will get for each day of the track meet. What is the fewest number of cases of bottled water Greg will need to provide for all the athletes, coaches, and judges at the track meet. Show your work or explain how you found your answer using equations. From PARCC PBA sample test #16 176

177 Division of Decimals Return to Table of Contents 177

178 Dividing Decimals To divide a decimal by a whole number: Use long division. Bring the decimal point up in the answer

179 Decimal Division Examples Match the quotient to the correct problem

180 88 Which answer has the decimal point in the correct location? A 1285 B C D

181 89 Which answer has the decimal point in the correct location? A 561 B 56.1 C 5.61 D

182 90 Which answer has the decimal point in the correct location? A 51 B 5.1 C 0.51 D

183 91 Select the answer with the decimal point in the correct location. A B C D E

184 92 Select the answer with the decimal point in the correct location. A 501 B 50.1 C 5.01 D E

185

186

187

188

189

190 Zero Place Holder Be careful, sometimes a zero needs to be used as a place holder can not go into 5. So, put a 0 in the quotient, and bring the 6 down. 190

191 98 What is the next step in this division problem? A B C Put a 2 in the quotient. Put a 0 in the quotient. Put a 1 in the quotient. 191

192 99 What is the next step in this division problem? A B Put a 0 in the quotient. Put a 2 in the quotient. C Bring down the

193 100 What is the next step in this division problem? 8. A B C Put a 0 in the quotient. Put a 4 in the quotient. Put a 2 in the quotient. 193

194

195

196 Zero Place Holder Be careful! Sometimes there is not enough to make a group, so zero in the quotient

197 103 What is the first step in this division problem? A B C Put a 0 in the ones place of the quotient. Put a 0 in the tenths place of the quotient. Put a 7 in the quotient. 197

198 104 What is the first step in this division problem? A B C Put a 0 in the quotient in the tenths and hundredths place. Put a 0 in the quotient in the ones place. Put a 4 in the quotient. 198

199

200 Another Way to Handle Remainders Instead of writing a remainder, continue to divide the remainder by the divisor (by adding zeros) to get additional decimal points Instead of leaving the 4 as a remainder, add a zero to the dividend. 200

201 Another Way to Handle Remainders Add a zero to the dividend. No remainder now. 201

202

203

204

205

206

207 Decimal Division Example When you have a remainder, you can add a decimal point and zeros to the end of a whole number dividend. Example: You want to save $284 over the next 5 months. How much money do you need to save each month? $284 5 = 207

208 Decimal Division Example 56 5 $ Don't leave the remainder 4, or write it as a fraction, add a decimal point and zeros to get the cents. 208

209 Decimal Division Example $ Since the answer is in money, write the answer as $

210 Decimal Division Example $ Since the answer is in money, add a decimal point and 3 zeros. Round the answer to the nearest cent (hundredths place). $82 7 = $

211 111 5 $63 211

212 112 $782 9 = 212

213 113 7 $

214 114 4 $

215 115 $48 22 = 215

216 To divide a number by a decimal: Change the divisor to a whole number by multiplying by a power of 10 Multiply the dividend by the same power of 10 Divide Divisor as a Decimal Bring the decimal point up in the answer Divisor Dividend 216

217 Divisor as Decimal Examples: Multiply by 10, so that 2.4 becomes must also be multiplied by Multiply by 100, so that.64 becomes must also be multiplied by

218 Divisor as Decimal Practice By what power of 10 should the divisor and dividend be multiplied?

219 Divisor as Decimal Examples By what power of 10 should the divisor and dividend be multiplied? means means 219

220

221 117 Divide = 221

222 118 Enter your answer = From PARCC EOY sample test #19 222

223 119 Enter your answer 6.3 x 0.1 = From PARCC EOY sample test #19 223

224

225 divided by

226 122 Yogurt costs $.50 each, and you have $7.25. How many can you buy? 226

227 Glossary & Standards Teacher Notes Return to Table of Contents 227

228 Standards for Mathematical Practices MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit. 228

229 Base Ten In a multi digit number, a digit in one place is ten times as much as the place to its right and 1/10 the value of the place to its left. Back to Instruction 229

230 Dividend The number being divided in a division equation Dividend 24 8 = 3 Dividend Dividend 24 8 = 3 Back to Instruction 230

231 Divisible When one number is divided by another, and the result is an exact whole number is divisible by 3 because 15 3 = 5 exactly = 5 R.1 Back to Instruction 231

232 Divisor The number the dividend is divided by. A number that divides another number without a remainder. 8 Divisor = 3 8 = 3 R1 24 Divisor Must divide evenly. Back to Instruction 232

233 Exponent A small, raised number that shows how many times the base is used as a factor. Exponent 3 2 Base "3 to the second power" 3 2 = 3 x = 3x 3x x x 3 3 Back to Instruction 233

234 Exponential Notation A number written using a base and an exponent. Standard 1,000 Word One Thousand Exponential 10 3 Back to Instruction 234

235 Number System A systematic way of counting numbers, where symbols/digits and their order represent amounts. Base Ten Roman Numerals Others Back to Instruction 235

236 Power of 10 Any integer powers of the number ten. (Ten is the base, the exponent is the power). 10 = 10x10 = 10x10x10 = = ,000 = = Back to Instruction 236

237 Quotient The number that is the result of dividing one number by another. Quotient 12 3 = 4 4 Quotient = Quotient 4 Back to Instruction 237

238 Remainder When a number is divided, the remainder is anything that is left over. (Anything in addition to the whole number.) 5 Remainder = 5 R R No remainder Back to Instruction 238

239 Standard Notation A general term meaning "the way most commonly written". A number written using only digits, commas and a decimal point. Standard 3.5 Word Three and five tenths Expanded Back to Instruction 239

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