4-3 Multiply Fractions. Multiply. Write in simplest form. SOLUTION: SOLUTION: SOLUTION: SOLUTION: esolutions Manual - Powered by Cognero Page 1

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1 1. Multiply. Write in simplest form esolutions Manual - Powered by Cognero Page 1

2 Financial Literacy Juanita spent of her allowance at the mall. Of the money spent at the mall, was spent on new earphones. What part of her allowance did Juanita spend on earphones? Find of. So, Juanita spent of her allowance on earphones. esolutions Manual - Powered by Cognero Page 2

3 8. A paint store has 35 gallons of paint in storage, of which are for outdoor use. The others are for indoor use. If each gallon costs $22, what is the total cost of the indoor paint in storage? Find the number of gallons of outdoor paint in storage. There are 14 gallons of outdoor paint in storage. So, there are or 21 gallons of indoor paint. Each gallon costs $22, so the total cost of the indoor paint in storage is $22 21, or $ Homeroom 101 and Homeroom 102 share a hallway bulletin board. If Homeroom 101 uses of their half to display artwork, what fraction of the bulletin board is used to display Homeroom 101 s artwork? Find of. So, of the bulletin board is used to display Homeroom 101 s artwork. 10. Use Math Tools Mr. Williams P.E. class lasts for hour. a. How many minutes are spent warming up and cooling down? b. How many minutes are not spent on instruction? Explain. a. Find of hour. esolutions Manual - Powered by Cognero Page 3

4 So, of an hour is spent warming up and cooling down. Convert this to minutes by multiplying by 60, which is the number of minutes in an hour. The class spent minutes warming up and cooling down. b. If of the time is spent on instruction, then of the -hr class is not. Find of. So, of an hour is not spent on instruction. Convert this to minutes by multiplying by 60, which is the number of minutes in an hour. So, 42 minutes are not spent on instruction. esolutions Manual - Powered by Cognero Page 4

5 11. Multiple Representations Use the bar diagram. a. WORDS Write a real-world problem represented by the bar diagram. b. MODELS Draw an area model to represent the situation. c. WORDS Explain how you would solve your problem. a. Sample answer: Olivia withdrew of her savings. She used of what was left to buy a book. If she had $100 in savings, how much did she spend on the book? b. c. Olivia used of the of her savings that was left to buy the book. Find of. Olivia spent of her savings on the book. Find of $100. So, Olivia spent $5 on the book. esolutions Manual - Powered by Cognero Page 5

6 12. Reason Inductively State whether each statement is true or false. If the statement is false, provide a counterexample. a. The product of two fractions that are each between 0 and 1 is also between 0 and 1. b. The product of a mixed number between 4 and 5 and a fraction between 0 and 1 is less than 4. c. The product of two mixed numbers that are each between 4 and 5 is between 16 and 25. a. True. The product of two fractions that are each between 0 and 1 is also between 0 and 1. The numerators of both fractions will both be less than their denominators. Therefore, the product of the numerators will always be less than the product of the denominators, which gives a number between 0 and 1. b. False. So, > 4. c. True. The value of 4 4 is 16 and the value of 5 5 is 25, so the product of two mixed numbers that are each between 4 and 5 is between 16 and Identify Structure If the product of two positive fractions a and b is, find three pairs of possible values for a and b. Sample answer. and and and esolutions Manual - Powered by Cognero Page 6

7 14. Persevere with Problems Justify why is equal to when b, c, d and e are not zero. The fraction can be simplified before multiplying by crossing out the factors that appear in both a numerator and a denominator, assuming none of the denominators are equal to zero. The factors that can be crossed out are b, c, and d. Thus, the only factors remaining are a in a numerator and e in a denominator, or. 15. Model with Mathematics Write a word problem in which you multiply a fraction by a number greater than 1. Estimate the product, then compare the product to your estimate. Sample answer: Makayla gives her cat cup of cat food each day. How much cat food will she have given her cat after 14 days?; Since is close to 1, Makayla will have given her cat about 1 14 or 14 cups of cat food.; 14 = which is close to 14. Multiply. Write in simplest form esolutions Manual - Powered by Cognero Page 7

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9 22. The bleachers at a football game are full, and of the fans in the bleachers are rooting for the home team. What fraction of the bleachers are filled with home-team fans? Justify your procedure. Find of. So, of the bleachers are filled with home-team fans. esolutions Manual - Powered by Cognero Page 9

10 23. The table shows the fraction of the votes that each candidate received. If 230 students voted, how many students voted for each candidate? of the 230 students voted for Nyemi. So, 138 students voted for Nyemi. of the 230 students voted for Luke. So, 69 students voted for Luke. of the 230 students voted for Natalie. So, 23 students voted for Natalie. esolutions Manual - Powered by Cognero Page 10

11 24. Model with Mathematics Alberto rode of the water rides at a water park. His sister, Reina, rode half of the rides that Alberto rode. What fraction of the water rides did Reina not ride? Support your answer with a model. Reina rode of the rides that Alberto rode, so she rode of of the water rides. So, Reina rode of the water rides. Therefore, she did not ride of the water rides. Five sixteenths of the square is shaded, which represents the number of rides Reina rode. So, the number of unshaded squares represents the rides she did not ride, or eleven sixteenths of the rides. 25. Justify Conclusions Lee is making oatmeal chocolate chip cookies and the recipe calls for cup of chocolate chips. If she wants to make procedure. of the recipe, what fraction of a cup of chocolate chips will she need? Justify your Lee needs of chocolate chips. Lee will need cup of chocolate chips to make of the recipe. esolutions Manual - Powered by Cognero Page 11

12 26. The table shows the fraction of votes each candidate received for Student Council president. If 180 students voted, fill in the table to show the number of votes each student received. To find the number of votes for each candidate, multiply the fraction by 180. David David had 36 votes Liam Liam had 54 votes Marta Marta had 18 votes Tiffany Tiffany had 72 votes esolutions Manual - Powered by Cognero Page 12

13 27. Four fifths of Terrence s text messages are to his friends. One half of those messages are to his friend Bianca. Terrance sends 120 text messages. How many text messages are to Bianca? So, or of Terrence s text messages are to Bianca. Terrence sends 48 messages to Bianca. Multiply = Multiply from left to right = 72 So, = 648. esolutions Manual - Powered by Cognero Page 13

14 = Multiply from left to right. So, = = Since multiplication can be performed in any order, group the numbers that you can multiply mentally. Multiply 8 by 11 first = 88 Next, multiply 88 by 15. So = 1,320. esolutions Manual - Powered by Cognero Page 14

15 31. Elise planted a row of flowers in an area with the dimensions shown. What is the area of her flower garden? To find the area of the flower garden, multiply 8 by. Remember to multiply the units of measure. feet feet = square feet So, the area of the flower garden is 4 square feet. 32. Without multiplying, determine whether the product of 5 is located on the number line at point A, B, or C. Explain your reasoning. A; The product must be less than 5 because the factors are 5 and a fraction less than 1. Since both points B and C are greater than 5, the answer must be point A. esolutions Manual - Powered by Cognero Page 15