1-2 Complex Fractions and Unit Rates. Simplify. SOLUTION: ANSWER: SOLUTION: ANSWER: SOLUTION: ANSWER: SOLUTION: ANSWER: SOLUTION: ANSWER: 6.
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1 1. Simplify esolutions Manual - Powered by Cognero Page 1
2 7. Mary is making pillows for her Life Skills class.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. 9. 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, the cost of the fabric was $6 per yard. $6 per yard So, Monica can read page per minute. 8. Doug entered a canoe race. He rowed miles in hour. What is his average speed in miles per hour? To find Doug's average speed, divide his miles rowed by his time. Write as. Write the percent as a fraction in simplest form. 10. % So, Doug rowed at a speed of 7 miles per hour. 7 miles per hour esolutions Manual - Powered by Cognero Page 2
3 11. % 13. A bank is offering home loans at an interest rate of %. Write the interest as a fraction in simplest form. 12. % So, the interest rate written as a fraction in simplest form is. esolutions Manual - Powered by Cognero Page 3
4 14. Be Precise Karl measured the wingspan of the butterfly and the moth shown below. How many times larger is the moth than the butterfly? 15. Construct an Argument 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. Sample answer: If one of the numbers in the ratio is a fraction, then the ratio can be a complex fraction. 16. Reason Inductively Write three different complex fractions that simplify to. Students should write three complex fractions that simplify to. Sample answer:,, To determine how many times larger the moth is, divide 3 by 3. Write 3 as and 3 as. Sample answer:,, 17. Persevere with Problems Use mental math to find the value of. So, the moth is times larger than the butterfly. Students should mentally write the expression as. Then they should notice the following: 124 in the first denominator and 124 in the third numerator divide to equal one, 230 in the second numerator and 230 in third denominator divide to equal one, and simplifies to. times larger esolutions Manual - Powered by Cognero Page 4
5 18. Justify Conclusions The value of a mutual fund increased by. Write as a fraction in simplest form. Justify your answer. Sample answer: Write as over 100. Then write as an improper fraction. Divide the numerator by the denominator. 19. Persevere with Problems The distance around the tire of a motorized scooter is inches. The tires make one revolution every second. Find the speed of the scooter in miles per hour. Round to the nearest tenth. (Hint: The speed of an object spinning in a circle is equal to the distance around the circle divided by the time it takes to complete one revolution.) mph. First change into a fraction, then divide by. Then change the units by multiplying by appropriate conversion rates. ; Sample answer: Write as over 100. Then write as an improper fraction. Divide the numerator by the denominator. mph esolutions Manual - Powered by Cognero Page 5
6 Simplify esolutions Manual - Powered by Cognero Page 6
7 A lawn company advertises that they can spread 7,500 square feet of grass seed in hours. Find the number of square feet of grass seed that can be spread per hour. To find the number of square feet of grass seed that can be spread per hour, divide 7,500 square feet of grass seed by 2 hours. 26. Mrs. Frasier is making costumes for the school play. Each costume requires 0.75 yard of fabric. She bought 6 yards of fabric. How many costumes can Mrs. Frasier make? To find the number of costumes Mrs. Frasier can make, divide the yards she bought by the amount of fabric required for each costume. Write 0.75 as. 3,000 square feet per hour Write the percent as a fraction in simplest form. 28. % So, Mrs. Frasier can make 8 costumes. 8 costumes esolutions Manual - Powered by Cognero Page 7
8 29. % 30. % 31. Justify Conclusions The value of a certain stock increased by %. Explain how to write % as fraction in simplest form. Students can refer to Example 5, Exercises 10-12, and Exercises to explain how to write 1 % as a complex fraction. Sample answer: Set 1 over 100. Write 1 as an improper fraction. Then divide the numerator by the denominator. ; Sample answer: Set over 100. Write as an improper fraction. Then divide the numerator by the denominator. 32. Debra bough yards of fabric at a remnant sale for $13. Determine if each of the following remnant deals have the same unit price as Debra's deal. Select yes or no. a. yards for $16 b. yards for $11 c. yards for $26 To find the unit price, divide the amount of money spent on each remnant by the number of yards. Debra's deal: Debra's deal was $4 per yard. a. esolutions Manual - Powered by Cognero Page 8
9 So, this is not the same deal. b. Which rider had the fastest rate of speed? Lorena; Determine each speed by dividing the distance by the time. Elena:. So, this is the same deal. c. Julio: So, this is the same deal. a. yards for $16 b. yards for $11 Kevin: c. yards for $ The table shows the distances traveled by 4 cyclists. Sort the speeds of the riders, in miles per hour, from slowest to fastest. Lorena: esolutions Manual - Powered by Cognero Page 9
10 36. 8 gallons = quarts There are 4 quarts in 1 gallon. So, there are 8 4 or 32 quarts in 8 gallons. 32 Fill in the box with the equivalent metric measurement meter = centimeters So, Lorena had the fastest rate of speed. Lorena; There are 100 centimeters in 1 meter liter = milliliters There are 1,000 milliliters in 1 liter. 1,000 Fill in the box with the equivalent customary measurement feet = inches There are 12 inches in 1 foot. So, there are 2 12 or 24 inches in 2 feet tons = pounds There are 2,000 pounds in 1 ton. So, there are 5 2,000 or 10,000 pounds in 5 tons. 10,000 esolutions Manual - Powered by Cognero Page 10
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