5-3 Complex Fractions and Unit Rates
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1 Simplify esolutions Manual - Powered by Cognero Page 1
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3 6. 7. Monica reads pages of a mystery book in 9 minutes. What is her average reading rate in pages per minute? To find Monica's reading rate, divide 7 by 9. Write 7 as. So, Monica can read page per minute. 8. Patrick drove 220 miles to his grandmother s house. The trip took him hours. What is his average speed in miles per hour? To find his average speed in miles per hour, divide 220 by. Write as. So, his average speed was 50 miles per hour. esolutions Manual - Powered by Cognero Page 3
4 Write each percent as a fraction in simplest form esolutions Manual - Powered by Cognero Page 4
5 Simplify. 13. esolutions Manual - Powered by Cognero Page 5
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9 25. Richard rowed a canoe miles in hour. What is his average speed in miles per hour? To find Richard's average speed, divide his miles rowed by his time. Write as. So, Richard rowed at a speed of 7 miles per hour. 26. A small airplane used gallons of fuel to fly a hour trip. How many gallons were used each hour? To find how many gallons were used each hour, divide the number of gallons used by the time. Write as and write as. So, the plane used gallons of fuel each hour. esolutions Manual - Powered by Cognero Page 9
10 27. Sally wants to make cookies for her little sister s tea party. Sally is cutting a roll of cookie dough into pieces that are inch thick. If the roll is inches long, how many cookies can she make? To find how many cookies she can make, divide the length of the roll of cookie dough by the thickness of one cookie. Write as. So, Sally can make 23 cookies. 28. Mary is making a curtain for her kitchen window. She bought yards of fabric. Her total cost was $15. What was the cost per yard? To find the cost per yard, divide $15 by 2 yards. Write 2 as. So, the cost of the fabric was $6 per yard. esolutions Manual - Powered by Cognero Page 10
11 Write the percent as a fraction in simplest form % esolutions Manual - Powered by Cognero Page 11
12 31. % 32. % 33. % esolutions Manual - Powered by Cognero Page 12
13 34. % 35. Mrs. Frasier is making costumes for the school play. The table shows the amount of material needed for each complete costume. She bought yards of material. a. How many complete costumes can she make? How much material will be left over? b. If she spent a total of $44.25 on fabric, what was the cost per yard? Explain how you solved. a. To find the amount of material needed for a complete costume, add the amounts needed for a top and bottom. So, one complete costume requires yards of material. To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of material required for each costume. Write as. esolutions Manual - Powered by Cognero Page 13
14 So, Mrs. Frasier can make 8 complete costumes with some material left over for of a costume. To find how much material will be left over, multiply by the amount of material needed for one complete costume. So, there will be yard left over. b. To find the cost per yard, divide the total cost by the number of yards purchased. So, the cost per yard was $3. esolutions Manual - Powered by Cognero Page 14
15 36. Financial Literacy The value of a certain stock increased by %. Write the percent as a fraction in simplest form. esolutions Manual - Powered by Cognero Page 15
16 37. A high school Family and Consumer Science class has pounds of flour with which to make soft taco shells. There are cups of flour in a pound, and it takes about cup of flour per shell. How many soft taco shells can they make? Convert the amount of flour that the class has from pounds to cups. So, the class has cups of flour. To find how many soft tacos the class can make, divide the total amount of flour by the amount of flour needed for one shell. So, the class can make about 140 soft taco shells. esolutions Manual - Powered by Cognero Page 16
17 38. Emma runs mile in 6 minutes. Joanie runs miles in 11 minutes. Whose speed is greater? Explain. Find Emma's rate by dividing the number of miles she ran by the number of minutes. So, Emma's rate is miles per minute. Find Joanie's rate by dividing the number of miles she ran by the number of minutes. So, Joanie's rate is about miles per minute. Joanie's speed is greater since > Financial Literacy A bank is offering home loans at an interest rate of %. Write the percent as a fraction in simplest form. So, the interest rate written as a fraction in simplest form is. esolutions Manual - Powered by Cognero Page 17
18 40. Justify Conclusions For a project, Karl measured the wingspan of the butterfly and a moth. His measurements are shown below. How many times larger is the moth than the butterfly? Justify your answer. To determine how many times larger the moth is, divide 3 by 3. Write 3 as and 3 as. So, the moth is times larger than the butterfly. esolutions Manual - Powered by Cognero Page 18
19 Simplify esolutions Manual - Powered by Cognero Page 19
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21 Identify Structure Write three different complex fractions that can be simplified to. Students should write three complex fractions that simplify to. Sample answer:,, esolutions Manual - Powered by Cognero Page 21
22 48. Persevere with Problems A motorized scooter has tires with circumference of 22 inches. The tires make one revolution every second. Find the speed of the scooter in inches per second. (Hint: The speed of an object spinning in a circle is equal to the circumference divided by the time it takes to complete one revolution.) To find the speed of the scooter, divide the circumference by the time it takes to complete one revolution. So, the speed of the scooter is 220 inches per second. 49. Building on the Essential Question Explain how complex fractions can be used to solve problems involving ratios. Students should recognize that complex fractions are fractions with a numerator, denominator, or both that are also fractions. So, if one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction. 50. Debra can run miles in hours. How many miles per hour can she run? A B C D miles per hour miles per hour miles per hour miles per hour To find the number of miles Debra can run per hour, divide 20 miles by 2 hours. Write 20 as and 2 as. Since Debra can run 9 miles per hour, D is the answer. esolutions Manual - Powered by Cognero Page 22
23 51. Tina wants to give away 6 bundles of thyme from her garden. If she has pound of thyme, how much will each bundle weigh? F lb G 3 lb H lb J 12 lb To determine how much each bundle weighs, divide pound by 6 bundles. So, each bundle weighs pound. H is the answer. 52. LaShondra is using a model to simplify the complex fraction below. Which statement shows how to use the model? The figure is divided into twelfths. Count A the twelfths that fit within of the figure. B C D The figure is divided into twelfths. Remove of the twelfths, and count those remaining. Count the number of thirds in the figure. Multiply this number by 12. Count the number of rectangles in the figure. Divide this number by 3. The figure represents the whole. Since there are 8 twelfths in of the figure, A is the answer. esolutions Manual - Powered by Cognero Page 23
24 Write each expression using exponents = ( 4) ( 4) ( 4) ( 4) ( 4) ( 4) ( 4) ( 4) = ( 4) m m m g g m m m g g = m 3 g (x + 1)(x + 1)(x + 1) (x + 1)(x + 1)(x + 1) = (x + 1) d d s s s s 5 5 d d s s s s = 5 2 d 2 s 4 Express each number in scientific notation ,000 80,000 = = esolutions Manual - Powered by Cognero Page 24
25 Financial Literacy A warehouse store sells two different sizes of the same brand of ketchup, a 114-ounce bottle and a 44-ounce bottle. Which size bottle is the better buy per ounce? Explain. Find the cost per ounce for the 114-ounce bottle by dividing the cost by the number of ounces The 114-ounce bottle costs about $0.03 per ounce. Find the cost per ounce for the 44-ounce bottle by dividing the cost by the number of ounces The 44-ounce bottle costs about $0.04 per ounce. The 144-ounce bottle is the better buy per ounce because $0.03 < $0.04. Classify each polygon with the name that best describes it. 66. This polygon is a rectangle because it has four sides, four right angles, and opposite sides of equal length. 67. This polygon is a trapezoid because it has four sides and exactly one pair of parallel sides. It is an isosceles trapezoid because the non-parallel sides are equal. esolutions Manual - Powered by Cognero Page 25
26 68. This polygon is a right triangle because it has three sides and one right angle. Replace each _ with <, >, or = to make a true sentence _ < _ > _ = 7.30 esolutions Manual - Powered by Cognero Page 26
3-2 Estimate Products. Estimate the product SOLUTION: Use rounding. So, is about SOLUTION: Use rounding.
Estimate the product. 1. 9.7 3.3 So, 9.7 3.3 is about 30. 2. 3.4 5.6 So, 3.4 5.6 is about 18. 3. 17.5 8.4 So, 17.5 8.4 is about 160. 4. 44.8 5.1 225 So, 44.8 5.1 is about 225. 5. 28.21 8.02 So, 28.21 8.02
The fractions 2_ 4, 3_
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