4-3 Add and Subtract Like Fractions. Add or subtract. Write in simplest form. SOLUTION: SOLUTION: SOLUTION: SOLUTION:

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1 1. Add or subtract. Write in simplest form esolutions Manual - Powered by Cognero Page 1

2 In Mr. Navarro s first period class, of the students got an A on their math test. In his second period class, of the students got an A. What fraction more of the students got an A in Mr. Navarro s first period class than in his second period class? Write in simplest form. Subtract the fraction of students who got an A in second period from the fraction of students who got an A in first period. more of the students got an A in Mr. Navarro s first period class than in his second period class. esolutions Manual - Powered by Cognero Page 2

3 8. To make a greeting card, Bryce used sheet of red paper, sheet of green paper, and sheet of white paper. How many sheets of paper did Bryce use? Bryce used sheets of paper. 9. The table shows the Instant Messenger abbreviations students at Hillside Middle School use the most. a. What fraction of these students uses LOL or CUL8R when using Instant Messenger? b. What fraction of these students uses L8R or BRB when using Instant Messenger? c. What fraction more of these students write L8R than CUL8R when using Instant Messenger? a. Add the fraction of students using LOL to the fraction of students using CUL8R. of these students uses LOL or CUL8R when using Instant Messenger. b. Add the fraction of students using L8R to the fraction of students BRB. of these students uses L8R or BRB when using Instant Messenger. c. Subtract the fraction of students who write CUL8R from the fraction of students who write L8R. more students write L8R than CUL8R. esolutions Manual - Powered by Cognero Page 3

4 10. Model with Mathematics Cross out the expression that does not belong. Explain your reasoning. or 1 Three of the expressions equal. cross out the expression since it equals or Justify Conclusions Select two like fractions with a difference of and with denominators that are not 3. Justify your selection. Students should select two like fractions with denominators that are multiples of 3 so that the difference is a fraction that simplifies to. Sample answer: and =, which simplifies to 12. Persevere with Problems Simplify the following expression. esolutions Manual - Powered by Cognero Page 4

5 First, identify the pattern of the terms in the expression. Starting with, add a like fraction with a numerator that is decreased by 1, then subtract a like fraction with a numerator that is decreased by 1, then add a like fraction with a numerator that is decreased by 1, and so on. Use the pattern to write the entire expression. Then simplify from left to right. esolutions Manual - Powered by Cognero Page 5

6 13. Justify Conclusions Is the difference between a positive like fraction and a negative like fraction always, sometimes, or never positive? Justify your answer with an example. always; Sample answer: 14. Use Math Tools Explain how you could use mental math to find the following sum. Then find the sum. Support your answer with a model. Sample answer: First, find the sum of the whole numbers, 21. Then group the fractions that have the same denominator together. Each group has a sum of 1: = 24; See students' work for model. 15. Persevere with Problems A construction company is replacing a window in a house. The window is currently 3 feet wide by 4 feet tall. The homeowner wants to add 9 inches to each side of the window. What is the new perimeter of the window in feet? Justify your reasoning ft; Sample answer: Since there is 12 inches in a foot, adding 9 inches to each side is adding ft to each side. or 17 ft Add or subtract. Write in simplest form. esolutions Manual - Powered by Cognero Page 6

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8 Two nails are inch and inch long. How much shorter is the -inch nail? Subtract. it is inch shorter. 23. Identify Structure Add. Write in simplest form. 24. Add numerators. or 1 esolutions Manual - Powered by Cognero Page 8

9 25. A recipe for Michigan blueberry pancakes calls for cup flour, cup milk, and cup blueberries. How much more flour is needed than milk? Write in simplest form. Subtract the amount of milk from the amount of flour. cup more flour is needed than milk. esolutions Manual - Powered by Cognero Page 9

10 26. The graph shows the location of volcanic eruptions. a. What fraction represents the volcanic eruptions for both North and South America? b. How much larger is the section for Asia and South Pacific than for Europe? Write in simplest form. a. Add the fractions for North and South America. represents the volcanic eruptions for both North and South America. b. Subtract the fraction for Europe from the fraction for Asia and South Pacific. the section for Asia and South Pacific is larger than the section for Europe by. esolutions Manual - Powered by Cognero Page 10

11 27. A group of friends bought two large pizzas and ate only part of each pizza. The picture shows how much was left. How many pizzas did they eat? Add the amount eaten from each pizza. the friends ate pizzas. esolutions Manual - Powered by Cognero Page 11

12 28. The table shows the results af a survey on students' favorite kind of movie. Select the appropriate values to complete the model to find the fraction of students that prefer comedy or action movies. What fraction of the students who were surveyed prefers comedy or action movies? First add up the number of students surveyed = 100 Set up the fraction of students who like comedy and the fraction of students who like action. Then, add the two fractions together. of the students prefer comedy or action movies. Fill in the with <, >, or = to make a true sentence. 29. Find equivalent fractions. The LCD is 8. Since,. esolutions Manual - Powered by Cognero Page 12

13 30. Find equivalent fractions. The LCD is 9. Since,. 31. Find equivalent fractions. The LCD is 35. Since,. 32. Find equivalent fractions. The LCD is 154. Since,. Find the least common denominator for the pair of fractions. 33. List the multiples of each denominator. 2: 2, 4, 6, 8, 10,... 3: 3, 6, 9, 12, 15,... Since the least common multiple is 6, the least common denominator is 6. esolutions Manual - Powered by Cognero Page 13

14 34. List the multiples of each denominator. 7: 7, 14, 21, 28, 35,... 28: 28, 56, 84,... Since the least common multiple is 28, the least common denominator is List the multiples of each denominator. 5: 5, 10, 15, 20, 25, 30,... 6: 6, 12, 18, 24, 30, 36,... Since the least common multiple is 30, the least common denominator is List the multiples of each denominator. 15: 15, 30, 45, 60, 75,... 12: 12, 24, 48, 60, 72,... Since the least common multiple is 60, the least common denominator is 60. esolutions Manual - Powered by Cognero Page 14

15 37. The results of a survey about favorite lunch choices are shown. Which lunch was chosen most often? The LCD is 50. Since, pizza was the lunch chosen most often. esolutions Manual - Powered by Cognero Page 15