3-6 Adding and Subtracting Unlike Fractions
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1 Find each sum. Write in simplest form esolutions Manual - Powered by Cognero Page 1
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3 Find each difference. Write in simplest form esolutions Manual - Powered by Cognero Page 3
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5 13. Dwayne needs cups of shredded cheese to put in his enchilada casserole and cup of cheese for the top. If he has 3 cups of cheese in all, how much cheese will he have left? To find how much cheese Dwayne used, find the sum of and. Subtract the result from 3 to find how much cheese Dwayne will have left. Dwayne will have cup of cheese left. Find each sum or difference. Write in simplest form. 14. esolutions Manual - Powered by Cognero Page 5
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8 During spring training, the Detroit Tigers won about of the games they played while the Cleveland Indians won of the games they played. What fraction more of the games did Detroit win than Cleveland? To find what fraction more of the games Detroit won than Cleveland, subtract from. So, Detroit won more games than Cleveland. esolutions Manual - Powered by Cognero Page 8
9 24. In a college dormitory, of the residents are juniors and of the residents are sophomores. What fraction of the students at the dormitory are juniors and sophomores? To find what fraction of the students in the dormitory are juniors and sophomores, find the sum of and. So, of the students in the dormitory are juniors and sophomores. Find each sum or difference. Write in simplest form. 25. esolutions Manual - Powered by Cognero Page 9
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13 34. Sybrina wants to make a 17-inch necklace with a -inch bead, a -inch bead and another -inch bead on it. What is the length of the remaining part of the necklace? To find the length of the remaining part of a necklace, first find the sum of the lengths of the beads on the necklace. Then, subtract the results from 17. So, the length of the remaining part of the necklace is 14 inches. 35. Kenzie is making three desserts for a party. The recipes call for cup of sugar, cups of sugar, and cups of sugar. If she has 6 cups of sugar, how much sugar will she have left over? To find how much sugar Kenzie will have left over, first add the sugar she will use in each recipe. Then, subtract the results from 6. So, Kenzie will have cup of sugar left over. esolutions Manual - Powered by Cognero Page 13
14 36. The length of a page in a yearbook is 10 inches. The top margin is inch, and the bottom margin is inch. What is the length of the page inside the margins? To find the length of the page inside the margins, first add the top and bottom margins. Then, subtract the result from 10. So, the length of the page inside the margins is inches. 37. MULTIPLE REPRESENTATIONS The perimeter of a geometric figure is the distance around the figure. You can find the perimeter of a rectangle by adding the measures of all four sides. a. Table Copy and complete the table below by listing the lengths and widths of three additional rectangles that have a perimeter of 20. b. Graph Write the values from the table as ordered pairs (l, w). Graph the ordered pairs on the coordinate plane. c. Numbers Use the graph to predict the length of a rectangle with a perimeter of 20 inches and a width of inches. Check the prediction by finding the actual length of the rectangle. a. To complete the table, find lengths and widths such that the sum of 2 times the length and 2 times the width is equal to 20. esolutions Manual - Powered by Cognero Page 14
15 b. To write the values from the table as ordered pairs, write the length first and then the width. The ordered pairs are (8, 2), (7, 3), (6, 4), (5, 5). Then, draw a graph of the first quadrant. The x-axis should go from 0 to 9 by 1 and the y -axis should go from 0 to 9 by 1. Graph the length on the x-axis and the width on the y -axis. The points appear to fall in a straight line. As the length increases, the width decreases. c. Using the graph, it appears that if the width is inches, the length should be between 4 and 5. Check a width of inches. So, if the width is inches, the length is inches. esolutions Manual - Powered by Cognero Page 15
16 38. Use the table to find the total average precipitation that falls in August, September, and October. To find the total average precipitation, add the precipitation for each month. So, the total average precipitation that falls in August, September, and October is inches. 39. Use the Internet or another source to find out the monthly rainfall totals in your community during the past year. How much rain fell in August, September, and October? 40. See Students work. Find each difference. Write in simplest form. esolutions Manual - Powered by Cognero Page 16
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19 46. The length of a rectangle is inches. The width is of the length. Find the width and the perimeter of the rectangle. Support your answer with a drawing. To find the width, multiply the length by. So, the width is inch. To find the perimeter, add the lengths of all of the sides. So, the perimeter is 8 inches. For drawing, see student s work. 47. Model with Mathematics Write a subtraction problem using unlike fractions with a least common denominator of 24. Find the difference. Fractions with denominators of 3 and 8 would have a least common denominator of Justify Conclusions Is the difference between a positive mixed number and a negative mixed number always, sometimes, or never positive? Justify your answer with an example. The difference between a positive mixed number and a negative mixed number is always positive, because subtracting a negative is the same as adding its opposite. esolutions Manual - Powered by Cognero Page 19
20 49. Construct an Argument Explain why you cannot add or subtract fractions with unlike denominators without renaming the fractions. You may use a diagram to illustrate your answer. Sample answer: Each of the fractions in the sum addends must be rewritten in the same unit before they can be added. uses a difference unit (parts of a whole). So the 50. Find the Error Cooper is adding the fractions,, and. His first step is to find the least common denominator of 3, 9, and 15. Find his mistake and correct it. Cooper found a common denominator but not the least. The least common denominator is Persevere with Problems A set of measuring cups has measures of 1 cup, cup, cup, cup, and cup. How could you measure cup of milk by using these measuring cups? Sample answer: Fill the -cup. From the -cup fill the -cup. will be left in the -cup because. esolutions Manual - Powered by Cognero Page 20
21 52. Building on the Essential Question Suppose you use 24 instead of 12 as a common denominator when finding. Will you get the correct answer? Explain. Yes, you will get the correct answer. There is an additional step involved at the end, reducing. esolutions Manual - Powered by Cognero Page 21
22 53. A recipe for snack mix contains cups of mixed nuts, cups of granola, and cup raisins. What is the total amount of snack mix? A c B c C c D c To find the total amount of snack mix, add the amount of mixed nuts, granola, and raisins. The total amount of snack mix is cups. So, Choice D is the correct answer. esolutions Manual - Powered by Cognero Page 22
23 54. SHORT RESPONSE The graph shows the results of an election for class president. What fraction of the votes did Michaela receive? To find the fraction of the votes that Michaela received, add the votes Sara and Mia received and subtract the results from 1. So, Michaela received of the votes. esolutions Manual - Powered by Cognero Page 23
24 55. The results of a grocery store survey are listed in the table. Find the fraction of families who grill out 2 or more times per month. F G H J To find the fraction of families who grill out 2 or more times per month, add the fraction of families who grill out 2 3 times a months and who grill out 4 or more times a month. The fraction of families who grill out 2 or more times per month is. So, Choice H is the correct answer. esolutions Manual - Powered by Cognero Page 24
25 56. Marco spent hour doing homework on Monday. On Tuesday, he spent hours doing homework. How long did he spend working on homework for those two days? A h B h C h D h To find how long Marco spent on homework on Monday and Tuesday, add the amount of time he spent on each of those days. Marco spent hours on homework on Monday and Tuesday. So, Choice D is the correct answer. Find each sum or difference. Write in simplest form. 57. esolutions Manual - Powered by Cognero Page 25
26 A 3-foot-long shelf is to be installed between two walls that are inches apart. How much of the shelf must be cut off so that it fits between the walls? There are 12 inches in a foot. So, there are 36 inches in 3 feet. To find how much of the shelf must be cut off, subtract from 36. So, inches must be cut off so that the shelf fits between the walls. Find each quotient. Write in simplest form. 61. esolutions Manual - Powered by Cognero Page 26
27 How many -pound hamburgers can be made from pounds of ground beef? To find the number of -pound hamburgers that can be made from pounds of ground beef, divide by. So, 11 hamburgers can be made. 65. A micron is a unit of measure that is approximately inch. Express this decimal as a fraction. The number is 39 millionths. So, =. Multiply (5 10) esolutions Manual - Powered by Cognero Page 27
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