6th Grade Fraction & Decimal Computation

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1 Slide 1 / 215

2 Slide 2 / 215 6th Grade Fraction & Decimal Computation

3 Slide 3 / 215 Fraction and Decimal Computation Fraction Division Long Division Review Adding Decimals Subtracting Decimals Distributive Property & Product of Decimals Multiplying Decimals Dividing Decimals Glossary & Standards Click on the topic to go to that section

4 Slide 4 / 215 Fraction Division Return to Table of Contents

5 Recall from 5th grade: Slide 5 / 215 Modeling Division When we are dividing, we are breaking apart into equal groups. Dividend Divisor = Quotient The model below represents: 8 4 = 2 2 groups of 4

6 Slide 6 / 215 Applying to Fractions The previous example used whole numbers and grouped the dividend according to the divisor. The same strategy can be applied when dividing with fractions. Use the model below to demonstrate: 8 1 = The pink rectangle represents 1. 2 See how many you can fit in the 8 squares.

7 Slide 7 / 215 Example Use the model below to demonstrate 2 1 =

8 Slide 8 / Evaluate the following problem using the model below. 3 1 =

9 Slide 9 / Evaluate the following problem using the model below. 5 1 =

10 Slide 10 / 215 Visual Model A fraction can be divided by a whole number using the following visual model. 3/ Divide into 4 groups

11 Slide 11 / 215 Word Problem The previous expression can be represented by the following word problem: How much will each person receive if 4 friends share a 3/5 pound bag of popcorn? Each friend will receive 3/20 lb. of popcorn.

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19 Slide 19 / 215 Vocabulary Review Complex Fraction: A fraction with another fraction in the numerator, denominator or both. Reciprocal: The inverse of a number/fraction. Original Number 4 Reciprocal 2

20 Slide 20 / 215 Patterns Do you notice a pattern between the division of fractions and their solution?

21 Slide 21 / 215 If you think about it, we are dividing by a fraction which creates a complex fraction. You need to eliminate the fraction in the denominator in order to solve the problem. To do this, multiply the numerator and denominator of the complex fraction by the reciprocal of the denominator (making the denominator = 1). You can then simplify the fraction by rewriting it without the denominator of 1 and solve the new multiplication problem.

22 Slide 22 / 215 Example = = x 3 2 x 3 2 = 1 2 x = 1 2 x 3 2 Original Complex Multiply by Simplify Rewrite Problem Fraction Reciprocal Denominator Without 1 There are rules that can be applied to fraction division problems to eliminate steps from this lengthy procedure. source -

23 Slide 23 / 215 Dividing Fractions Algorithm Algorithm Step 1: Leave the first fraction the same. Step 2: Multiply the first fraction by the reciprocal of the second fraction. Step 3: Simplify your answer = 5 x 2 1 = 1 x 2 5 x 1 = 2 5

24 Slide 24 / 215 Dividing Fractions Algorithm Some people use the saying " Keep Change Flip" to help them remember the algorithm. Change Keep Flip Changed Kept Flipped = 3 5 x 8 7 = 3 x 8 5 x 7 = 24 35

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26 Slide 26 / 215 Checking Your Answer To check your answer, use your knowledge of fact families = = x is 7 8 of 24 35

27 Slide 27 / ) = 5 4 x 8 10 True False

28 Slide 28 / ) = True False

29 Slide 29 / ) = A 1 B C

30 10 ) Slide 30 / 215

31 11 ) Slide 31 / 215

32 Slide 32 / 215 Simplify Sometimes you can cross simplify prior to multiplying. without cross simplifying with cross simplifying

33 Slide 33 / Can this problem be cross simplified? Yes No

34 Slide 34 / Can this problem be cross simplified? Yes No

35 Slide 35 / Can this problem be cross simplified? Yes No

36 Slide 36 / Can this problem be cross simplified? Yes No

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41 Slide 41 / 215 Visual Model A mixed number can be divided by a mixed number using the following visual model. First find the least common denominator (LCD) which is 6. If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?

42 Slide 42 / 215 Visual Model Since our LCD is 6, every 6 lines is considered a whole. 1 1/2 is equivalent to 9 sections on the number line. 1 1/ /3 2 2/3 is equivalent to 16 sections on the number line. So 1 1/2 2 2/3 = 9/16

43 Slide 43 / 215 Visual Model What if the problem were written as? 2 2/ /2 1 1/2 How many times does 1 1/2 divide into 2 2/3?

44 Slide 44 / 215 Dividing Mixed Numbers Algorithm Step 1: Rewrite the Mixed Number(s) as an improper fraction(s). (write whole numbers / 1) Step 2: Follow the same steps for dividing fractions = = 6 x 2 = 12 =

45 Slide 45 / 215 Example Evaluate: = = 5 3 x 2 7 = 10 21

46 Slide 46 / ) =

47 Slide 47 / ) =

48 Slide 48 / ) =

49 Slide 49 / ) =

50 Slide 50 / 215 Application Problem Winnie needs pieces of string for a craft project. How many 1/6 yd pieces of string can she cut from a piece that is 2/3 yd long? x 6 1 = 12 3 = pieces or x 6 1 = = 4 pieces

51 Slide 51 / 215 Application Problem One student brings 1/2 yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbons will each student receive? x 1 3 = 1 6 yards of ribbon

52 Slide 52 / 215 Application Problem Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs can she cut? x 4 3 = = = 1 8 rungs

53 Slide 53 / 215 Application Problem A box weighing 9 1/3 lb contains toy robots weighing 1 1/6 lb apiece. How many toy robots are in the box? x = 8 1 = 8 robots

54 Slide 54 / Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion? A 8 pounds B 4 1/2 pounds C 2/5 pounds D 1/8 pound

55 Slide 55 / A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel? A 84 miles B 62 miles C 42 miles D 38 miles

56 Slide 56 / One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use? A 48 tablespoons B 24 tablespoons C 12 tablespoons D 6 tablespoons

57 Slide 57 / A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book? A 5/12 pound B 2 2/5 pounds C 8 2/5 pounds D 86 2/5 pounds

58 Slide 58 / There is gallon of distilled water in the class science supplies. If each pair of students doing an experiment uses gallon of distilled water, there will be gallon left in the supplies. How many students are doing the experiments?

59 Slide 59 / Carol makes cups of snack mix. She puts all the snack mix into plastic bags. She puts cup of the snack mix in each bag. How many plastic bags does Carol need? Enter your answer in the box. bags From PARCC EOY sample test non-calculator #9

60 Slide 60 / Part A A group of hikers buy 8 bags of trail mix. Each bag contains cups of trail mix. The trail mix is shared evenly among 12 hikers. How many cups of trail mix will each hiker receive? Show your work or explain your answer. From PARCC PBA sample test calculator #10

61 Slide 61 / Part B The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout. Determine the total distance each hiker will hike. Show your work or explain your answer. From PARCC PBA sample test calculator #10

62 Slide 62 / Part B (continued) Determine the total number of gallons of water each hiker will bring. Show your work or explain your answer. From PARCC PBA sample test calculator #10

63 Slide 63 / This diagram shows a number line. Part A James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board. From PARCC PBA sample test calculator #8

64 Slide 64 / Part B Write an equation using division that represents how James can find the number of pieces he can cut from the board. From PARCC PBA sample test calculator #8

65 Slide 65 / 215 Long Division Review Return to Table of Contents

66 Slide 66 / 215 Some division terms to remember... The number to be divided into is known as the dividend The number which divides the other number is known as the divisor The answer to a division problem is called the quotient 20 5 = 4 4 quotient divisor 5 20 dividend 20 5 = 4

67 Slide 67 / 215 When we are dividing, we are breaking apart into equal groups EXAMPLE 1 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

68 Slide 68 / 215 Step 3: Check your answer. click 44 x 3 132

69 Slide 69 / 215 Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track What place value should we round to? Round to the largest place value. click 357 rounds to 15 rounds to Our answer should approximately be... click 20

70 Slide 70 / 215 EXAMPLE 2 (change pages to see each step) Step 1: Can 15 go into 3, no so can 15 go into 35, yes x 2 = = 5 Compare 5 < 15

71 Slide 71 / 215 EXAMPLE 2 (change pages to see each step) Step 2 : Bring down the 7. Can 25 go into 207, yes x 3 = =12 Compare 12 < 15

72 Slide 72 / 215 EXAMPLE 2 (change pages to see each step) Step 3: You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division x 8 = = 0 Compare 0 < 15 Is our answer close to our estimate?

73 Slide 73 / 215 Check your answer x 15 click 357

74 Slide 74 / 215 Estimate the following problems. Discuss your answers with your group. click click click click 15 20

75 Slide 75 / 215 Now solve the following problems. Discuss your answers with your group. click click click click

76 Slide 76 / Estimate the quotient

77 Slide 77 / Compute =

78 Slide 78 / Estimate the quotient. 1,551 55

79 Slide 79 / Compute. 1, =

80 Slide 80 / Estimate the quotient. 1,288 35

81 Slide 81 / Compute. 1, =

82 Slide 82 / The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.

83 Slide 83 / The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?

84 Slide 84 / Compute =

85 Slide 85 / The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?

86 Slide 86 / Compute =

87 Slide 87 / Compute =

88 Slide 88 / Enter your answer in the box. 34, = From PARCC EOY sample test non-calculator #18

89 Slide 89 / 215 Adding Decimals Return to Table of Contents

90 Slide 90 / 215 Adding Decimals If you know how to add whole numbers then you can add decimals. Just follow these few steps. Step 1: Put the numbers in a vertical column, aligning the decimal points. Step 2: Add each column of digits, starting on the right and working to the left. Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.

91 Slide 91 / 215 Adding Decimals When adding or subtracting decimals, always remember to align the decimals vertically

92 Slide 92 / 215 Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track What place value should we round to? Round to the nearest whole number. click 5.1 rounds to 1.25 rounds to 0.04 rounds to 1.99 rounds to Our answer should approximately be... 8 click

93 Slide 93 / 215 Adding Decimals Now, try this - Don't forget - LINE THEM UP You can add a zero as a place holder to help line your numbers up.

94 Slide 94 / 215 TRY THESE. Estimate the following sums in your notebook. Check with the rest of your group. 1) ) click = 12 click = 24 3) ) click click = = 18

95 Slide 95 / 215 TRY THESE. Complete in your notebook then check with the rest of your group. 1) ) click click 3) ) click click

96 Slide 96 / Add the following: = A 6.1 B C 1.15 D 0.16

97 Slide 97 / Joanne and Peter are working together to solve the problem Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why? A Joanne B Peter

98 Slide 98 / Find the sum =

99 Slide 99 / Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $ Estimate how much Franco spent on the video games.

100 Slide 100 / Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $ How much did he spend on video games?

101 Slide 101 / What is the sum of and ? A B C D

102 Slide 102 / Estimate the sum A 20 B 21 C 22 D 23

103 Slide 103 / Find the sum = A B C D 20.14

104 Slide 104 / Five students collected paper to be recycled. Shelly's stack was.008 cm. thick; Ken's stack was.125 cm. thick; Joe's stack was.150 cm. thick; Betty's stack was.185 cm. thick; Mary's stack was.005 cm. thick. What was the thickness of the papers collected to be recycled? A.561 cm. B.452 cm. C.480 cm. D.473 cm.

105 Slide 105 / Find the sum =

106 Slide 106 / What is the sum of and 2.67? Enter your answer in the box. From PARCC EOY sample test non-calculator #19

107 Slide 107 / 215 Web Link Let's go to Cool Math and practice addition. Cool Math Link

108 Slide 108 / 215 Subtracting Decimals Return to Table of Contents

109 Slide 109 / 215 Subtracting Decimals If you know how to subtract whole numbers then you can subtract decimals. Just follow these few steps. Step 1: Step 2: Put the numbers in a vertical column, aligning the decimal points Subtract the numbers from right to left using the same rules as whole numbers Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.

110 Slide 110 / 215 Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track What place value should we round to? Round to the nearest whole number. click 21.7 rounds to 8.21 rounds to Our answer should approximately be click

111 Slide 111 / 215 Subtracting Decimals What do we do if there aren't enough decimal places when we subtract? Don't forget...line Them Up! What goes here?

112 Slide 112 / 215 TRY THESE. Estimate the following differences in your notebook. Then check with the rest of your group. 1) ) click 8-0 = 8 click 12-9 = 3 3) ) click 17-8 = 9 click 10-5 = 5

113 Slide 113 / 215 TRY THESE. Complete in your notebook then check with the rest of your group. 1) ) click click ) ) click click

114 59 ) = Slide 114 / 215

115 60 ) = Slide 115 / 215

116 Slide 116 / Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit? A $20 B $18 C $13 D $12

117 Slide 117 / Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit? A $37.57 B $12.43 C $13.57 D $12.00

118 63 ) = Slide 118 / 215

119 Slide 119 / The Johnson twins raced each other in the 200-meter dash. Jordan finished in seconds, and Max finished in seconds. How much faster was Jordan than Max?

120 Slide 120 / Timothy is working on the problem He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not? Yes No

121 66 ) = Slide 121 / 215

122 67 ) = Slide 122 / 215

123 Slide 123 / Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths? A B C D

124 Slide 124 / If you buy two movie tickets for $8.25 each, what will your change be from $20?

125 Slide 125 / 215 Web Link Let's go to Cool Math and practice subtraction. Cool Math Link

126 Slide 126 / 215 The Distributive Property and the Product of Decimals Return to Table of Contents

127 Slide 127 / 215 If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step 1: Ignore the decimal points. Multiplication Step 2: Multiply the numbers using the same rules as whole numbers. Step 3: Count the total number of digits to the right of the decimal point. Put that many digits to the right of the decimal point in your answer.

128 Evaluate 200 x 41.5 Slide 128 / 215 Distributive Property 8,300 click We can also use the distributive property to calculate the product. Separate 41.5 into an addition expression with two addends Apply the distributive property Apply the order of operations 200 x x ( ) (200 x 41) + (200 x 0.5) 8, = 8,300

129 Slide 129 / 215 Distributive Property Evaluate 400 x x ( + ) (400 x ) + (400 x ) + = 7332 This method is known as partial products.

130 Slide 130 / 215 Distributive Property How can we use partial products to calculate the area of the rectangle shown below? ft ft 0.6 ft 200 x ft ft 200 x ( + ) (200 x ) + (200 x ) + = 11,720 Click to reveal

131 Slide 131 / ) 12(43) = 12(40) x 12(3) True False

132 Slide 132 / Use the distributive property to rewrite the expression. 3(76.8) Students type their answers here

133 Slide 133 / Calculate the product using partial products. 5(48)

134 Slide 134 / Calculate the product using partial products. 13(5.2)

135 Slide 135 / Calculate the product using partial products. 300(7.4)

136 Slide 136 / Calculate the product using partial products. 200(6.5)

137 Slide 137 / Calculate the area of the rectangle using partial products. 300 units 43.9 units

138 Slide 138 / 215 Multiplying Decimals Return to Table of Contents

139 Slide 139 / 215 Multiplication Convert the following decimal numbers into fractions. 0.7 x 0.09 What is the product? click We multiplied seven tenths by nine hundredths. What place value will the last digit in the product be in if we convert it into a decimal number? click Thousandths

140 Slide 140 / 215 Try These! What place value will the last digit be in for the following problems? Don't forget to convert them to fractions first. Fractions Product Place Value 1) 0.3 x 0.7 2) 0.2 x ) 0.08 x 0.231

141 Slide 141 / 215 Multiplication Do you notice a pattern for multiplying decimals? 3.5 x x x Where does the decimal point go? Drag the decimal point

142 Slide 142 / 215 Multiplication If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step 1: Ignore the decimal points. Step 2: Step 3: Multiply the numbers using the same rules as whole numbers. Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer.

143 Slide 143 / 215 Multiplication 3.21 x.04 } 2 digits } 2 digits.1284 There are a total of four digits to the right of the decimal points. There must be four digits to the right of the decimal point in the answer.

144 Slide 144 / 215 Estimate Your Answer Before any calculations, estimate your answer to make sure you are on the right track x 4.04 What place value should we round to? Round to the nearest whole number. click 23.2 rounds to 4.04 rounds to Our answer should approximately be... click 92

145 Slide 145 / 215 Exact Answer 23.2 } 1 digit x 4.04 } 2 digits There are a total of three digits to the right of the decimal points. There must be three digits to the right of the decimal point in the answer. Estimating helps us recognize where the decimal point belongs!

146 Slide 146 / 215 Estimate Your Answer Estimate your answer for the following problem by rounding the numbers to the nearest whole number. 9.5 x rounds to What is your estimate? 0.05 rounds to For problems like these, use your number sense! You are multiplying 9.5 by 0.05 which means you are taking a part (fraction) of 9.5. So your answer must be smaller than 9.5! click

147 Slide 147 / 215 TRY THESE. Estimate the following products in your notebook then check with the rest of your group. 1) ) 8.31 x 4.21 x click click 15 x 4 = 60 8 x 1 = 8 3) ) x 5.2 x click 7 x 5 = 35 click smaller than 3.214

148 Slide 148 / 215 TRY THESE. Complete in your notebook then check with the rest of your group. 1) ) 8.31 x 4.21 x click click 3) ) x 5.2 x click click

149 Slide 149 / Estimate the product x A The product will be less than 1 B The product will be equal to 1 C The product will be greater than 1

150 Slide 150 / The product of 0.42 x will have 4 digits to the right of the decimal point. True False

151 79 Multiply 0.42 x Slide 151 / 215

152 80 Multiply x 2.1 Slide 152 / 215

153 Slide 153 / You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money? Estimate to determine your answer. Do not solve. Yes No

154 Slide 154 / You need to buy 6 notebooks that cost $0.87 each. How much will this cost?

155 83 Multiply x Slide 155 / 215

156 Slide 156 / The regular price of a pair of jeans is $ Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $ What would the total cost be of four pairs of jeans on sale? A $ B $90.00 C $86.00 D $52.49

157 Slide 157 / How many digits will be to the right of decimal point the product for the problem x 7.8? A 2 B 3 C 4 D 5

158 86 Multiply x 7.8 Slide 158 / 215

159 87 Multiply x 0.21 Slide 159 / 215

160 Slide 160 / Enter your answer in the box x 4.39 = From PARCC EOY sample test non-calculator #7

161 Slide 161 / Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event. How much profit, in dollars, will Thomas earn if he sells all the bottles of water? Enter your answer in the box. $ From PARCC EOY sample test non-calculator #17

162 Slide 162 / 215 Dividing Decimals Return to Table of Contents

163 Slide 163 / 215 Divide Decimals by Whole Numbers Step 1: Use long division. Step 2: Bring the decimal point up into the quotient

164 Slide 164 / 215 Try This! =

165 Slide 165 / The Power of Ten Multiplying by a power of ten makes dividing by decimals easier! 1) 13 x 10 = 2) 94 x 100 = 3) 28 x 1000 = 4) 6.2 x 10 = 5) 4.78 x 100 = 6) x 1000 = Do you see a pattern for multiplying by a power of ten? The decimal point moves to the right depending on the number of zeros Click in the to power of ten! Reveal

166 Slide 166 / 215 Divide by Decimals Step 1: Change the divisor to a whole number by multiplying by a power of 10. Step 2: Multiply the dividend by the same power of 10. Step 3: Step 4: Use long division. Bring the decimal point up into the quotient. Divisor Quotient Dividend

167 Slide 167 / 215 Power of Ten Try rewriting these problems so you are ready to divide! Multiply by 10, so that 15.6 becomes must also be multiplied by Multiply by 1000, so that.234 becomes must also be multiplied by 1000

168 Slide 168 / 215 Power of Ten Rewrite each problem after multiplying by a power of 10. 1) click click 2) click 3) ) click

169 Slide 169 / 215 Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track What place value should we round to? Round to the nearest whole number. click 23.2 rounds to 4.04 rounds to Our answer should approximately be... click 5

170 Slide 170 / 215 Try This! Be sure to round your answer to the thousandths click

171 Slide 171 / 215 Estimate Estimate your answer for the following problem by rounding the numbers to the nearest whole number rounds to What is your estimate? 0.05 rounds to For problems like these, use your number sense! If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5? Your answer must be greater than 9.5! click

172 Slide 172 / Divide =

173 Slide 173 / Use estimation to figure out if the quotient will be A less than B around C greater than 4.866

174 Slide 174 /

175 93 ) 10 divided by 0.25 = Slide 175 / 215

176 94 ) = Slide 176 / 215

177 Slide 177 /

178 Slide 178 / Estimate

179 Slide 179 / Evaluate =

180 Slide 180 / Estimate

181 Slide 181 / Evaluate =

182 Slide 182 / Enter your answer in the box = From PARCC EOY sample test #2 non-calculator

183 Slide 183 / 215 Terminating and Repeating There are two types of decimals - terminating and repeating. A terminating decimal is a decimal that ends. All of the examples we have completed so far are terminating. A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern. To denote a repeating decimal, a line is drawn above the numbers that repeat. However, with a calculator, the last digit is rounded.

184 Slide 184 / 215 Terminating or Repeating Let's consider the following... Click to Reveal

185 Slide 185 / 215 Repeating Example Click to Reveal

186 Slide 186 / 215 Repeating Example Click to Reveal

187 101 ) Slide 187 / 215

188 102 ) = Slide 188 / 215

189 Slide 189 / You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy?

190 Slide 190 / ) = A 2.27 B C 22.7 D 22.72

191 105 Slide 191 / 215

192 Slide 192 / If 6 people are on an elevator and together they weigh pounds, find the average weight of each person.

193 107 ) = Slide 193 / 215

194 Slide 194 / Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?

195 109 Slide 195 / 215

196 110 ) = Slide 196 / 215

197 Slide 197 / Texas suffered through a heat wave in August The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, and What was the average temperature for those four days?

198 Slide 198 / For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?

199 Slide 199 / ) A 40.9 B C D 40.9

200 Slide 200 / 215 Glossary & Standards Return to Table of Contents

201 Slide 201 / 215 Algorithm A step-by-step process to find a solution. How to... Step 1: Step 2: Step 3: = Add the ones then add the tens It's like a cooking recipe for mathematics. Back to Instruction

202 Slide 202 / 215 Average The value/amount of each item when the total is distributed across each item equally = 9 = 9 3 = 3 Back to Instruction

203 Slide 203 / 215 Complex Fraction A fraction whose numerator or denominator or both contain fractions = = Must be written as a fraction. Back to Instruction

204 Slide 204 / 215 Cross Simplify Used to make operations with fractions easier. Divide the numerator of one fraction and the denominator of another fraction by their GCF GCF of 5 and 15 is = Back to Instruction

205 Slide 205 / 215 Distributive Property Multiplying a sum by a number is the same as multiplying each addend in the sum by the same number and then adding the products. 5 3 (3 + 2) 3x5=3(3+2) (3+4)= (2x3)+(2x4) also applies to subtraction a(b-c)=ab-ac a(b+c)=ab+ac Back to Instruction

206 Slide 206 / 215 Dividend The number being divided in a division equation Dividend 24 8 = 3 Dividend Dividend 24 8 = 3 Back to Instruction

207 Slide 207 / 215 Divisor The number the dividend is divided by. A number that divides another number without a remainder Divisor 24 8 = 3 Divisor 25 8 = 3 R 1 Must divide evenly. Back to Instruction

208 Slide 208 / 215 Power of 10 Any integer powers of the number ten. (Ten is the base, the exponent is the power.) 10 = 10x10 = 10x10x10 = = 10 2 = = 1,000 Back to Instruction

209 Slide 209 / 215 Profit The difference between the amount earned and the amount spent. Earned - Spent Profit $30 Washing Cars $12 - Supplies $18 Profit Back to Instruction

210 Slide 210 / 215 Quotient The number that is the result of dividing one number by another = 4 4 Quotient 3 12 Quotient 12 3 = Quotient 4 Back to Instruction

211 Slide 211 / 215 Reciprocal One of two numbers whose product is one. 1 x 1 = 1 1 is the reciprocal of 1. Number 2 x 1 2 = 1 Reciprocal r x r = 1 Back to Instruction

212 Slide 212 / 215 Repeating Decimal A decimal with a digit or group of digits that repeats endlessly =.3 33 =.21 3 ( ) Back to Instruction

213 Slide 213 / 215 Terminating Decimal A decimal that ends and doesn't go on forever. 1/2 =.5 3/8 = Back to Instruction

214 Slide 214 / 215 Vertical In an up-down position. vertical horizontal diagonal Back to Instruction

215 Slide 215 / 215 Standards for Mathematical Practice MP1: Making sense of problems & persevere in solving them. MP2: Reason abstractly & 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 & make use of structure. MP8: Look for & express regularity in repeated reasoning. Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.

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