🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning # Prealgebra ## Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price ## Chapter 5 ## Rational Numbers ## Educators ### Problem 1 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{7}{8}$$ Sarah W. Numerade Educator ### Problem 2 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{3}{5}$$ Sarah W. Numerade Educator ### Problem 3 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{5}{16}$$ Sarah W. Numerade Educator ### Problem 4 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$1 \frac{3}{20}$$ Sarah W. Numerade Educator ### Problem 5 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$2 \frac{2}{5}$$ Sarah W. Numerade Educator ### Problem 6 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$6 \frac{3}{4}$$ Sarah W. Numerade Educator ### Problem 7 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{2}{3}$$ Sarah W. Numerade Educator ### Problem 8 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-\frac{5}{9}$$ Sarah W. Numerade Educator ### Problem 9 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$4 \frac{2}{11}$$ Sarah W. Numerade Educator ### Problem 10 In$2004,$the San Francisco 49ers led the NFL in converting on 14 of 19 fourth downs. To the nearest thousandth, what part of the time did the 49ers convert on fourth down? Sarah W. Numerade Educator ### Problem 11 Replace each with$<,>,$or$=$to make a true sentence. $$\frac{9}{10} \circ 0.90$$ Sarah W. Numerade Educator ### Problem 12 Replace each with$<,>,$or$=$to make a true sentence. $$0.3 \circ \frac{1}{3}$$ Sarah W. Numerade Educator ### Problem 13 Replace each with$<,>,$or$=$to make a true sentence. $$-\frac{3}{4} \circ-\frac{7}{8}$$ Sarah W. Numerade Educator ### Problem 14 Seven-fiftieths of water usage comes from leaky plumbing and$\frac{3}{20}$come from faucets. Does a greater fraction of water usage come from leaky plumbing or from faucets? Sarah W. Numerade Educator ### Problem 15 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{1}{5}$$ Sarah W. Numerade Educator ### Problem 16 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{7}{20}$$ Sarah W. Numerade Educator ### Problem 17 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-\frac{8}{25}$$ Sarah W. Numerade Educator ### Problem 18 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-\frac{5}{8}$$ Sarah W. Numerade Educator ### Problem 19 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$7 \frac{3}{10}$$ Sarah W. Numerade Educator ### Problem 20 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$1 \frac{1}{2}$$ Sarah W. Numerade Educator ### Problem 21 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-5 \frac{1}{8}$$ Sarah W. Numerade Educator ### Problem 22 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-3 \frac{3}{4}$$ Sarah W. Numerade Educator ### Problem 23 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{1}{9}$$ Sarah W. Numerade Educator ### Problem 24 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$\frac{2}{9}$$ Sarah W. Numerade Educator ### Problem 25 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-\frac{5}{11}$$ Sarah W. Numerade Educator ### Problem 26 Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-\frac{4}{11}$$ Sarah W. Numerade Educator ### Problem 27 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. Sarah W. Numerade Educator ### Problem 28 During the$2003-2004$season, Kevin Weekes of the Carolina Hurricanes saved 1506 out of 1652 shots on goal. To the nearest thousandth, what part of the time did Weekes save shots on goal? Sarah W. Numerade Educator ### Problem 29 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$0.3 \circ \frac{1}{4}$$ Sarah W. Numerade Educator ### Problem 30 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$\frac{5}{8} \circ 0.65$$ Sarah W. Numerade Educator ### Problem 31 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$\frac{2}{5} \circ 0.4$$ Sarah W. Numerade Educator ### Problem 32 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$0.3 \circ \frac{1}{2}$$ Sarah W. Numerade Educator ### Problem 33 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$\frac{7}{8} \circ \frac{8}{9}$$ Sarah W. Numerade Educator ### Problem 34 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$\frac{5}{7} \circ \frac{10}{14}$$ Sarah W. Numerade Educator ### Problem 35 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-\frac{1}{8} \circ-\frac{1}{10}$$ Sarah W. Numerade Educator ### Problem 36 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-\frac{6}{25} \circ-\frac{1}{4}$$ Sarah W. Numerade Educator ### Problem 37 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$\frac{1}{5} \circ 0 . \overline{5}$$ Sarah W. Numerade Educator ### Problem 38 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$1 \frac{1}{20} \circ 1.01$$ Sarah W. Numerade Educator ### Problem 39 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$3 \frac{4}{9} \circ 3 . \overline{4}$$ Sarah W. Numerade Educator ### Problem 40 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$6.18 \circ 6 \frac{1}{5}$$ Sarah W. Numerade Educator ### Problem 41 For Exercises 41 and 42 use the graph at the right. Did more or less than one-fourth of an inch of rain fall on Tuesday? Explain. Sarah W. Numerade Educator ### Problem 42 For Exercises 41 and 42 use the graph at the right. Suppose it rained$\frac{9}{10}$inch on Saturday. How does this compare to the previous five days? Sarah W. Numerade Educator ### Problem 43 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-0.75 \circ-\frac{7}{9}$$ Sarah W. Numerade Educator ### Problem 44 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$\frac{34}{99} \circ 0.3 \overline{4}$$ Sarah W. Numerade Educator ### Problem 45 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-2 \frac{1}{12} \circ-2.09$$ Sarah W. Numerade Educator ### Problem 46 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-\frac{5}{16} \circ-\frac{8}{25}$$ Sarah W. Numerade Educator ### Problem 47 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-2.2 \circ-2 \frac{2}{7}$$ Sarah W. Numerade Educator ### Problem 48 Replace each$\circ$with$<,>,$or$=$to make a true sentence. $$-5 \frac{1}{3} \circ-5 \frac{3}{10}$$ Sarah W. Numerade Educator ### Problem 49 Of all the cars sold in the United States in$2003, \frac{2}{5}$were imported from Japan and 0.26 were imported from Germany. Are more Japanese or German cars sold in the United States? Explain. Sarah W. Numerade Educator ### Problem 50 Order each group of numbers from least to greatest. $$\frac{7}{8}, 0.8, \frac{7}{9}$$ Sarah W. Numerade Educator ### Problem 51 Order each group of numbers from least to greatest. $$-0.29,-\frac{3}{11},-\frac{2}{7}$$ Sarah W. Numerade Educator ### Problem 52 Order each group of numbers from least to greatest. $$2 \frac{3}{5}, 2.67,2 \frac{2}{3}$$ Sarah W. Numerade Educator ### Problem 53 Order each group of numbers from least to greatest. $$-1 . \overline{1},-1 \frac{1}{8},-1 \frac{1}{10}$$ Sarah W. Numerade Educator ### Problem 54 Find a fraction or mixed number that might represent each point on the graph at the right. Sarah W. Numerade Educator ### Problem 55 For Exercises 55 and$56,$use the following information. Write$\frac{5}{6}$as a decimal rounded to the nearest hundredth. Sarah W. Numerade Educator ### Problem 56 For Exercises 55 and$56,$use the following information. Which form of the number is best to use? Explain. Sarah W. Numerade Educator ### Problem 57 Give one example each of real-world situations where it is most appropriate to give a response in fractional form and in decimal form. Sarah W. Numerade Educator ### Problem 58 Find a terminating and a repeating decimal between$\frac{1}{6}$and$\frac{8}{9} .$Explain how you found them. Sarah W. Numerade Educator ### Problem 59 Write the prime factorization of each denominator and the decimal equivalent of each fraction. Then explain how prime factors of denominators and the decimal equivalents of fractions are related. $$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{8}, \frac{1}{9}, \frac{1}{10}, \frac{1}{12}, \frac{1}{15}, \frac{1}{20}$$ Check back soon! ### Problem 60 Luke is making lasagna that calls for$\frac{4}{5}$pound of mozzarella cheese. The store only has packages that contain 0.75 - 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. Sarah W. Numerade Educator ### Problem 61 Explain how 0.5 and$0 . \overline{5}$are different. Which is greater? Sarah W. Numerade Educator ### Problem 62 Which decimal represents the shaded portion of the figure? A 0.6 B$0 . \overline{6}$C 0.63 D$0.6 \overline{3}$ Sarah W. Numerade Educator ### Problem 63 The fraction$\frac{7}{9}$is found between which pair of fractions on a number line? F.$\frac{3}{5}$and$\frac{3}{4}$G.$\frac{7}{10}$and$\frac{4}{5}$H.$\frac{7}{10}$and$\frac{3}{4}$J.$\frac{3}{5}$and$\frac{2}{3}$ Sarah W. Numerade Educator ### Problem 64 Write each number in scientific notation. $$854,000,000$$ Sarah W. Numerade Educator ### Problem 65 Write each number in scientific notation. $$0.077$$ Sarah W. Numerade Educator ### Problem 66 Write each number in scientific notation. $$0.00016$$ Sarah W. Numerade Educator ### Problem 67 Write each number in scientific notation. $$925,000$$ Sarah W. Numerade Educator ### Problem 68 Write each expression using a positive exponent. $$10^{-5}$$ Sarah W. Numerade Educator ### Problem 69 Write each expression using a positive exponent. $$(-2)^{-7}$$ Sarah W. Numerade Educator ### Problem 70 Write each expression using a positive exponent. $$x^{-4}$$ Sarah W. Numerade Educator ### Problem 71 Write each expression using a positive exponent. $$y^{-3}$$ Sarah W. Numerade Educator ### Problem 72 Write$(a \cdot a \cdot a)(a \cdot a)\$ using an exponent. Sarah W.

### Problem 73

A car travels an average of 464 miles on one tank of gas. If the tank holds 16 gallons, how many miles per gallon does it get? Sarah W.

### Problem 74

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? Sarah W.

### Problem 75

Simplify each fraction.
$$\frac{4}{30}$$ Sarah W.

### Problem 76

Simplify each fraction.
$$\frac{5}{65}$$ Sarah W.

### Problem 77

Simplify each fraction.
$$\frac{36}{60}$$ Sarah W.

### Problem 78

Simplify each fraction.
$$\frac{12}{18}$$ Sarah W.

### Problem 79

Simplify each fraction.
$$\frac{21}{24}$$ Sarah W.

### Problem 80

Simplify each fraction.
$$\frac{16}{28}$$ Sarah W.

### Problem 81

Simplify each fraction.
$$\frac{32}{48}$$ Sarah W.
$$\frac{125}{1000}$$ 