3-1 Fractions and Decimals

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1 1. Write each fraction as a decimal. Use a bar to show a repeating decimal. So, = So, = So, = So, = So, =. esolutions Manual - Powered by Cognero Page 1

2 6. So, =. 7. FOOTBALL In one season, the New England Patriots converted 16 of 20 fourth downs. What part of the time did the Patriots convert on fourth down? So, = 0.8. The Patriots convert 0.8 of their fourth downs. Replace each _ with <, >, or = to make a true sentence _ Write as a decimal and then compare the decimals. Since 0.89 is to the right of on a number line, 0.89 >. 9. _ Since is to the left of 0.6 on a number line, <. esolutions Manual - Powered by Cognero Page 2

3 _ Write as a decimal and then compare the decimals. Since 0.21 is to the left of 0.2 on a number line, <. 11. _ Since is to the right of on a number line, >. 12. _ 0.61 Write as a decimal and then compare the decimals. Since 0.6 is to the right of 0.61 on a number line, > esolutions Manual - Powered by Cognero Page 3

4 13. _ Since 0.75 is to the left of on a number line, <. 14. WATER USAGE Of Nikki s home water usage, comes from lawn watering, and comes from cooking. Does a greater fraction of water usage come from lawn watering or from cooking? On a number line, 0.14 is to the left of So, 0.14 < 0.15, and therefore cooking than on watering her lawn.. Nikki uses more water on 15. SCHOOL On his first reading test, Tre answered questions correctly. On his second reading test, he answered questions correctly. On which test did Tre have the better score? On a number line, is to the right of So, > 0.85, and therefore. Tre scored better on the first test. esolutions Manual - Powered by Cognero Page 4

5 16. Write each fraction as a decimal. Use a bar to show a repeating decimal. So,. 17. So,. 18. So,. 19. So,. 20. So,. esolutions Manual - Powered by Cognero Page 5

6 21. So,. 22. So,. 23. So,. 24. So,. 25. So,. esolutions Manual - Powered by Cognero Page 6

7 26. So,. 27. So,. 28. BUSINESS The customer service department resolved 106 of 120 customer complaints in a one-hour time span. To the nearest thousandth, find the resolve rate of the customer service department. So, The resolve rate of the customer service department is about HOCKEY In a recent season, Niklas Backstrom of the Minnesota Wild saved 955 out of 1028 shots on goal. To the nearest thousandth, what part of the time did Backstrom save shots on goal? So, Niklas Backstrom saved about of the shots on goal. esolutions Manual - Powered by Cognero Page 7

8 Replace each _ with <, >, or = to make a true sentence. 30. _ 0.4 Write as a decimal and then compare the decimals. Since both values are equal to 0.4, _ Write as a decimal and then compare the decimals. Since 0.7 is to the left of 0.85 on a number line,. 32. _ Since is to the left of on a number line,. esolutions Manual - Powered by Cognero Page 8

9 33. _ Since both values are equal to,. 34. _ Since is to the right of 0.25 on a number line,. 35. _ Since is to the left of 0.1 on a number line,. esolutions Manual - Powered by Cognero Page 9

10 36. _ Write as a decimal and then compare the decimals. Since is to the right of on a number line,. 37. _ 0.67 Write as a decimal and then compare the decimals. Since 0.5 is to the left of 0.67 on a number line,. esolutions Manual - Powered by Cognero Page 10

11 WEATHER The graph below shows the amount of rain, in inches, that fell in a 5-day period. 38. On which days did it rain less than one-fifth of an inch? Mon Tues Wed Thurs Fri It rained less than one-fifth of an inch on Monday, Wednesday, and Friday. esolutions Manual - Powered by Cognero Page 11

12 39. Did more or less than one-fourth inch of rain fall on Tuesday? Explain. On Tuesday, 0.28 inch of rain fell. = 0.25 and 0.28 > 0.25 So, more than one-fourth inch of rain fell on Tuesday. 40. Suppose it rained inch on Saturday. How does this compare to the previous five days? = 0.93 The total amount of rain for Monday through Friday was 0.93 inch. There was less rain on Saturday than during the total of the previous 5 days because = 0.9 and 0.9 < Replace each _ with <, >, or = to make a true sentence. 41. _ Write as a decimal and then compare the decimals. Since is to the left of on a number line,. esolutions Manual - Powered by Cognero Page 12

13 42. _ Write as a decimal and then compare the decimals. Since both values are equal to,. 43. _ Write as a decimal and then compare the decimals. Since is to the right of on a number line,. 44. _ Since is to the right of 0.32 on a number line,. esolutions Manual - Powered by Cognero Page 13

14 _ Write as a decimal and then compare the decimals. Since 2.2 is to the right of on a number line,. 46. _ Since is to the left of 5.3 on a number line,. 47. CARPENTRY A carpenter has some bolts that are marked,,,, and. If all measurements are in inches, how should these bolts be arranged from least to greatest? < < < 0.5 < 0.75 Ordered from least to greatest, the bolt sizes are,,,,. esolutions Manual - Powered by Cognero Page 14

15 Order each group of numbers from least to greatest ,, Ordered from least to greatest, the numbers are 0.29,,. 49., 2.67, Ordered from least to greatest, the numbers are,, ,, Ordered from least to greatest, the numbers are,,. esolutions Manual - Powered by Cognero Page 15

16 51.,, Ordered from least to greatest, the numbers are,, SOFTBALL The table shows the number of times at bat and hits that players on Rawson Middle School team had last season. Order the players based on their batting averages from greatest to least. (Hint: Divide the number of hits by the number of at bats.) Player Kristen Batting Average Cho Brooke Alma Jessica From greatest to least batting average, the players are Jessica, Alma, Kristen, Brooke, and Cho. Write each decimal using bar notation esolutions Manual - Powered by Cognero Page 16

17 MULTIPLE REPRESENTATIONS Use the number line shown. a. Numerical Find a fraction or mixed number that might represent each point on the graph. b. Algebraic Write an inequality using two of your values. Sample answers: a. A is slightly greater than B is located close to 0.9, which is. C is slightly less than = 1.2 D is slightly greater than = 1.3 E is slightly greater than 1.5. = 1.6 The points could be A: ; B: ; C: ; D: ; E:. b. A is located to the left of B on the number line, so the fraction that represents A is less than the fraction that represents B. < esolutions Manual - Powered by Cognero Page 17

18 58. JEWELRY The table shows the number of each type of bead on 3 bracelets that Mrs. Fraser made for a craft show. Which bracelet has the greatest fraction of glass beads? the least? Bracelet Total Beads Fraction of Glass Beads = = = 27 Bracelet 1 has the greatest fraction of glass beads. Bracelet 2 has the least. 59. OPEN ENDED Give one example each of real-world situations where it is most appropriate to give a response in fractional form and in decimal form. Sample answer: Fractional form is appropriate to use in customary measurement, whereas decimal form is appropriate to use for a stock price. 60. CHALLENGE Are there any rational numbers between and? Explain. Because and are equal, there are no rational numbers between these two values. esolutions Manual - Powered by Cognero Page 18

19 61. CHALLENGE A unit fraction is a fraction that has 1 as its numerator. Write the four greatest unit fractions that are repeating decimals. Write each fraction as a decimal. The four greatest unit fractions that are repeating decimals are. 62. WRITING IN MATH Luke is making lasagna that calls for pound of mozzarella cheese. The store only has packages that contain and 0.85-pound of mozzarella cheese. Which of the following techniques might Luke use to determine which package to buy? Justify your selection(s). Then use the technique(s) to solve the problem. Mental math: Since = 0.8, he should buy the 0.85-pound package so he ll have enough cheese for the lasagna. 63. CHALLENGE Write the following fractions as decimals:,, and. Make a conjecture about how to express these kinds of fractions as decimals. Sample answer: When the denominator is a 9 or 99, the numerator repeats. 64. WRITING IN MATH Explain how 0.5 and are different. Which is greater? 0.5 = 0.50 and = ; is greater because in the hundredths place, 5 > 0. esolutions Manual - Powered by Cognero Page 19

20 65. Sherman answered of the multiple-choice question on his science test correctly. Write this fraction as a decimal. A 0.4 B 0.45 C 0.8 D 4.5 So, = 0.8. Choice C is correct. 66. Which of the following show the fractions,,,, and in order from least to greatest? F,,,, G,,,, H,,,, J,,,, Ordered from least to greatest, the fractions are,,,,. Choice H is correct. esolutions Manual - Powered by Cognero Page 20

21 67. The fraction is found between which pair of fractions on a number line? A B C D and and and and Write as a decimal. Find which values A lies between., so it is not found between these two values. B is found between these two values. C, so it is not found between these two values. D, so it is not found between these two values. Choice B is correct. esolutions Manual - Powered by Cognero Page 21

22 68. SHORT RESPONSE Which items shown in the table have a recycle rate less than one half? Material Paper Fraction Recycled Compare to Aluminum Cans Glass Paper and glass have a recycle rate that is less than one half. Find each product or quotient ( 12)( 5) 70. 2(42)(3) ( 6) 54 ( 6) = 9 esolutions Manual - Powered by Cognero Page 22

23 ( 9) 72 ( 9) = SCUBA DIVING A scuba diver descends from the surface of the lake at a rate of 6 meters per minute. Where will the diver be in relation to the lake s surface after 4 minutes? The diver descended 6 meters every minute. This can be represented by the integer 6. To find where the diver will be in relation to the lake s surface after 4 minutes, multiply 6 by = 24 So, the diver will be 24 feet or 24 feet below the surface after 4 minutes. 74. EMPLOYMENT The scatter plot shows the years of experience and salaries of twenty people. Does the data show a positive, negative, or no relationship? Explain. The data appears to go uphill from left to right. As the years of experience increase, the salary increases. This shows a positive relationship. Evaluate each expression if x = 7, y = 3, and z = x + y + z 76. 4x z esolutions Manual - Powered by Cognero Page 23

24 77. 6y z 78. 9x + 8y Write each decimal in word form is written as thirty-four hundredths is written as five and eight hundred, thirty-six thousandths. 0.3 is written as three-tenths is written as two and eight hundred seventy-five thousandths. esolutions Manual - Powered by Cognero Page 24

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