4-5 Add and Subtract Mixed Numbers. Add or subtract. Write in simplest form. SOLUTION: SOLUTION: Rename using the LCD, 12.
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1 1. Add or subtract. Write in simplest form. 2. Rename using the LCD, Rename using the LCD, Rename using the LCD, 12. esolutions Manual - Powered by Cognero Page 1
2 6. Since is less than, rename as before subtracting. 7. Rename using the LCD, 15. Since is less than, rename as. before subtracting. 8. Rename using the LCD, 6. Since is less than, rename as before subtracting. 9. Rename 8 as before subtracting. esolutions Manual - Powered by Cognero Page 2
3 Justify Conclusions Choose an operation to solve the problem. Explain your reasoning. Then solve the problem. Write your answer in simplest form. 10. If Juliana and Brody hiked both of the trails listed in the table, how far did they hike? To find the distance hiked altogether, add. Rename using the LCD, 6. So, Juliana and Brody hiked miles altogether. 11. The length of Kasey s garden is feet. Find the width of Kasey s garden if it is feet shorter than the length. Because the width is shorter than the length, subtract. Since is less than, rename as before subtracting. So, the garden is feet wide. 12. Karen wakes up at 6:00 A.M. It takes her hours to shower, get dressed, and comb her hair. It takes her hour to eat breakfast, brush her teeth, and make her bed. At what time will she be ready for school? Add the time it takes for Karen to shower, get dressed, and comb her hair to the time it takes for Karen to eat breakfast, brush her teeth, and make her bed. Rename using the LCD, 4. Because hours is 1 hour and 45 minutes, and Karen woke up at 6:00 A.M., add 1 hour and 45 minutes to 6:00 A.M. 6:00 A.M. + 1 h 45 min = 7:45 A.M. So, Karen will be ready at 7:45 A.M. esolutions Manual - Powered by Cognero Page 3
4 Add or subtract. Write in simplest form Rename using the LCD, 9. esolutions Manual - Powered by Cognero Page 4
5 16. Rename using the LCD, Model with Mathematics Write a real-world problem that could be represented by the expression. Then solve your problem. Sample answer: A board with length feet needs to be cut from a -foot existing board. How much wood will be left after the cut is made?; ft 18. Persevere with Problems A string is cut in half. One of the halves is thrown away. One fifth of the remaining half is cut away and the piece left is 8 feet long. How long was the string initially? Justify your answer. Make a few educated guesses to determine the initial length of the string. For each guess, go through the procedure described in the problem, and see if your end result is 8 feet. If the initial string is 20 feet and cut in half, the two halves would each be 10 feet. Cutting one fifth of one of these 10-foot halves would require splitting the 10 feet into five equal parts. Each part would be 2 feet. So, cutting one fifth of 10 feet would be the same as cutting 2 feet. The remaining portion would be 8 feet long. esolutions Manual - Powered by Cognero Page 5
6 19. Model with Mathematics Using three mixed numbers as side lengths, draw an equilateral triangle with a perimeter of Sample answer: feet. Add or subtract. Write in simplest form. 20. Since is less than, rename as before subtracting. 21. Rename using the LCD, 24. esolutions Manual - Powered by Cognero Page 6
7 22. Rename 13 as before subtracting Rename using the LCD, 20. Since is less than, rename as before subtracting. 25. Rename using the LCD, 8. Since is less than, rename as before subtracting. esolutions Manual - Powered by Cognero Page 7
8 Justify Conclusions Choose an operation to solve. Explain your reasoning. Then solve the problem. Write your answer in simplest form. 26. The length of Alana's hair was inches. After her haircut, the length was inches. How many inches did she have cut? Because cutting her hair makes it shorter, subtract. Rename using the LCD, 4. So, Alana had inches cut off her hair. 27. Emeril used a total of cups of flour to make three pastries. He used cups of flour for the first and cups for the second. How much flour did Emeril use for the third pastry? Because you are given the total and want to find a part of the total, subtract. So, the third pastry uses cups of flour. esolutions Manual - Powered by Cognero Page 8
9 28. Margarite made the jewelry shown. If the necklace is inches longer than the bracelet, how long is the necklace? Because the length of the bracelet is known, and the length of the necklace is inches longer than the bracelet, add. Rename using the LCD, 8. So, the necklace is inches long. 29. Find the perimeter of the figure. Write your answer in simplest form. So, the perimeter of the figure is yards. esolutions Manual - Powered by Cognero Page 9
10 30. Suppose you want to place a shelf that is inches long in the center of a wall that is inches wide. About how far from each edge of the wall should you place the shelf? Since the question says about you can round to 30 and to 46. Then subtract the length of the shelf from the width of the wall and divide by 2 to find the distance from each edge of the wall = = 8 So, about 8 inches. 31. A recipe for snack mix calls for cups of cereal. The amount of peanuts needed is cups less than the amount of cereal needed. Complete each box below to make a true statement. The recipe calls for cups of peanuts. A total of cups of peanuts and cereal are needed in all. The amount of peanuts needed is less than the cereal needed, so subtract from using the LCD of 12. So, cups of peanuts are needed. To determine the total amount of peanuts and cereal is needed, add to using the LCD of 12. So, there is a total of cups of peanuts and cereal needed. esolutions Manual - Powered by Cognero Page 10
11 32. Maria practiced the piano for hours last week and hours this week. Use the bar diagram sections to construct a bar diagram that represents how many hours Maria practiced in the past two weeks. How many hours did Maria practice the piano in the past 2 weeks? Notice that it takes 4 of the small bars to equal 1 of the large bar. Therefore, the small bar represents large bar represents 1. Using this, the bar diagram looks like: and the To determine how many hours Maria practiced the past two weeks, count the number of bars on the right side of the equation. 4 large bars represents 4 and one small bar represents, so the total number of hours Maria practiced was. Round the mixed number to its nearest whole number. Then estimate the product esolutions Manual - Powered by Cognero Page 11
12 35. Zoe s average running speed is about miles per hour. Suppose Zoe runs for hours. About how far will she have run? Explain. miles is about 7 miles and 7 2 = 14 So, Zoe will have to run about 14 miles. hours is about 2 hours. esolutions Manual - Powered by Cognero Page 12
4-4 Multiply Mixed Numbers. Multiply. Write in simplest form. SOLUTION: SOLUTION: SOLUTION: SOLUTION: esolutions Manual - Powered by Cognero Page 1
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