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1 Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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3 Lesson 5-1 Lesson 5-2 Lesson 5-3 Lesson 5-4 Lesson 5-5 Lesson 5-6 Lesson 5-7 Lesson 5-8 Lesson 5-9 Lesson 5-10 Writing Fractions as Decimals Rational Numbers Multiplying Rational Numbers Dividing Rational Numbers Adding and Subtracting Like Fractions Least Common Multiple Adding and Subtracting Unlike Fractions Measures of Central Tendency Solving Equations with Rational Numbers Arithmetic and Geometric Sequences

4 Click the mouse button or press the Space Bar to display the answers.

5 Example 1 Write a Fraction as a Terminating Decimal Example 2 Write a Mixed Number as a Decimal Example 3 Write Fractions as Repeating Decimals Example 4 Compare Fractions and Decimals Example 5 Compare Fractions to Solve a Problem

6 Write as a decimal. Method 1 Use paper and pencil. Answer:

7 Write as a decimal. Method 2 Use a calculator ENTER Answer:

8 Write as a decimal. Answer: 0.375

9 Write as a decimal. Write as the sum of an integer and a fraction. Add. Answer: 1.25

10 Write as a decimal. Answer: 2.6

11 Write as a decimal. The digits 12 repeat. Answer:

12 Write as a decimal. The digits 18 repeat. Answer:

13 a. Write as a decimal. Answer: b. Write as a decimal. Answer:

14 Replace with <, >, or = to make a true sentence. Write the sentence. Write as a decimal. In the tenths place,. Answer: On a number line, 0.7 is to the right of 0.65, so.

15 Replace with <, >, or = to make sentence. a true Answer: <

16 Grades Jeremy got a score of on his first quiz and on his second quiz. Which grade was the higher score? Write the fractions as decimals and then compare the decimals. Quiz #1: Quiz #2: Answer: The scores were the same, 0.80.

17 Baking One recipe for cookies requires of a cup of butter and a second recipe for cookies requires of a cup of butter. Which recipe uses less butter? Answer: the second recipe

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19 Click the mouse button or press the Space Bar to display the answers.

20 Example 1 Write Mixed Numbers and Integers as Fractions Example 2 Write Terminating Decimals as Fractions Example 3 Write Repeating Decimals as Fractions Example 4 Classify Numbers

21 Write as a fraction. Answer: Write as an improper fraction.

22 Write 10 as a fraction. Answer:

23 a. Write as a fraction. Answer: b. Write 6 as a fraction. Answer:

24 Write 0.26 as a fraction or mixed number in simplest form is 26 hundredths. Answer: Simplify. The GCF of 26 and100 is 2.

25 Write as a fraction or mixed number in simplest form is 2 and 875 thousandths. Answer: Simplify. The GCF of 875 and 1000 is 125.

26 Write each decimal as a fraction or mixed number in simplest form. a Answer: b Answer:

27 Write as a fraction in simplest form. Let N represent the number. Multiply each side by 100 because two digits repeat. Subtract N from 100N to eliminate the repeating part,

28 Divide each side by 99. Simplify. Answer: Check ENTER

29 Write as a fraction in simplest form. Answer:

30 Identify all sets to which the number 15 belongs. Answer: 15 is a whole number, an integer, a natural number, and a rational number.

31 Identify all sets to which the number belongs. Answer: is a rational number.

32 Identify all sets to which the number belongs. Answer: is a nonterminating, repeating decimal. So, it is a rational number.

33 Identify all sets to which each number belongs. a. 7 Answer: integer, rational b. Answer: rational c Answer: rational

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35 Click the mouse button or press the Space Bar to display the answers.

36 Example 1 Multiply Fractions Example 2 Simplify Before Multiplying Example 3 Multiply Negative Fractions Example 4 Multiply Mixed Numbers Example 5 Multiply Algebraic Fractions Example 6 Use Dimensional Analysis

37 Find. Write the product in simplest form. Multiply the numerators. Multiply the denominators. Answer: Simplify. The GCF of 10 and 40 is 10.

39 Find. Write the product in simplest form. Divide 8 and 6 by their GCF, 2. Multiply the numerators and multiply the denominators. Answer: Simplify.

40 Find. Write the product in simplest form. Answer:

41 Find. Write the product in simplest form. Divide 2 and 4 by their GCF, 2. Multiply the numerators and multiply the denominators. Answer: Simplify.

43 Find. Write the product in simplest form. Rename and rename. Divide by the GCF, 3. Multiply. Answer: Simplify.

44 Find. Write the product in simplest form. Answer:

45 Find. Write the product in simplest form. The GCF of and q is q. Answer: Simplify.

46 Find. Write the product in simplest form. Answer:

47 Track The track at Cole s school is mile around. If Cole runs one lap in two minutes, how far (in miles) does he run in 30 minutes? Words Distance equals the rate multiplied by the time. Variables Let d = distance, r = rate, and t = time. Formula d = rt

48 mile per 2 minutes 30 minutes Write the formula Divide by the common factors and units. Multiply. Simplify. Answer: Cole runs miles in 30 minutes.

49 Check The problem asks for the distance. When you divide the common units, the answer is expressed in miles. So, the answer is reasonable.

50 Walking Bob walks mile in 12 minutes. How far does he walk in 30 minutes? Answer:

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52 Click the mouse button or press the Space Bar to display the answers.

53 Example 1 Find Multiplicative Inverses Example 2 Divide by a Fraction Example 3 Divide by a Whole Number Example 4 Divide by a Mixed Number Example 5 Divide by an Algebraic Fraction Example 6 Use Dimensional Analysis

54 Find the multiplicative inverse of. The product is 1. Answer: The multiplicative inverse or reciprocal of.

55 Find the multiplicative inverse of. Write as an improper fraction. The product is 1. Answer: The reciprocal of.

56 Find the multiplicative inverse of each number. a. Answer: b. Answer:

57 Find. Write the quotient in simplest form. Multiply by the multiplicative inverse of,. Divide 5 and 10 by their GCF, 5. Answer: Simplify.

58 Find. Write the quotient in simplest form. Answer:

59 Find. Write the quotient in simplest form. Write 3 as. Multiply by the multiplicative inverse of,. Answer: Multiply the numerators and multiply the denominators.

60 Find. Write the quotient in simplest form. Answer:

61 Find. Write the quotient in simplest form. Rename the mixed numbers as improper fractions. Multiply by the multiplicative inverse of,. Divide out common factors. Answer: Simplify.

62 Find. Write the quotient in simplest form. Answer:

63 Find. Write the quotient in simplest form. Multiply by the multiplicative inverse of,. Divide out common factors. Answer: Simplify.

64 Find. Write the quotient in simplest form. Answer:

65 Travel How many gallons of gas are needed to travel miles if a car gets miles per gallon? To find how many gallons, divide.

66 Write as improper fractions. Multiply by the reciprocal of Divide out common factors. Simplify.

67 Answer: gallons of gas are needed. Check Use dimensional analysis to examine the units. Divide out the units. Simplify. The result is expressed as gallons. This agrees with your answer of gallons of gas.

68 Sewing Emily has yards of fabric. She wants to make pillows which each require yards of fabric to complete. How many pillows can Emily make? Answer: or 8 pillows

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70 Click the mouse button or press the Space Bar to display the answers.

71 Example 1 Add Fractions Example 2 Add Mixed Numbers Example 3 Subtract Fractions Example 4 Subtract Mixed Numbers Example 5 Add Algebraic Fractions

72 Find. Write the sum in simplest form. Estimate The denominators are the same. Add the numerators. Answer: Simplify and rename as a mixed number.

73 Find. Write the sum in simplest form. Answer:

74 Find. Write the sum in simplest form. Add the whole numbers and fractions separately. Add the numerators. Answer: Simplify.

75 Find. Write the sum in simplest form. Answer:

76 Find. Write the difference in simplest form. Estimate The denominators are the same. Subtract the numerators. Answer: Simplify.

77 Find. Write the difference in simplest form. Answer:

78 Evaluate. Estimate Replace r with and q with. Write the mixed numbers as improper fractions. Subtract the numerators. Answer: Simplify.

80 Find. Write the sum in simplest form. The denominators are the same. Add the numerators. Add the numerators. Answer: Simplify.

81 Find. Write the sum in simplest form. Answer:

82

83 Click the mouse button or press the Space Bar to display the answers.

84 Example 1 Find the LCM Example 2 The LCM of Monomials Example 3 Find the LCD Example 4 Find the LCD of Algebraic Fractions Example 5 Compare Fractions

85 Find the LCM of 168 and 180. Number Prime Factorization Exponential Form The prime factors of both numbers are 2, 3, 5, and 7. Multiply the greatest powers of 2, 3, 5, and 7 appearing in either factorization. Answer: The LCM of 168 and 180 is 2520.

86 Find the LCM of 144 and 96. Answer: 288

87 Find the LCM of. Multiply the greatest power of each prime factor. Answer: The LCM of.

88 Find the LCM of. Answer:

89 Find the LCD of. Write the prime factorization of 8 and 20. Highlight the greatest power of each prime factor. Multiply. Answer: The LCD of.

90 Find the LCD of. Answer: 36

91 Find the LCD of. Answer: The LCD of.

92 Find the LCD of Answer:

93 Replace with <, >, or = to make a true statement. The LCD of the fractions is. Rewrite the fractions using the LCD and then compare the numerators. Multiply the fraction by to make the denominator 105. Multiply the fraction by to make the denominator 105.

94 Answer: Since, then. is to the left of on the number line.

95 Replace with <, >, or = to make a true statement. Answer: <

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97 Click the mouse button or press the Space Bar to display the answers.

98 Example 1 Add Unlike Fractions Example 2 Add Fractions Example 3 Add Mixed Numbers Example 4 Subtract Fractions Example 5 Subtract Mixed Numbers Example 6 Use Fractions to Solve a Problem

99 Find. Use as the common denominator. Rename each fraction with the common denominator. Answer: Add the numerators.

101 Find. Estimate The LCD is 30. Rename each fraction with the LCD. Add the numerators. Answer: Simplify.

103 Find. Write in simplest form. Write the mixed numbers as improper fractions. Rename fractions using the LCD, 24. Simplify.

106 Find. The LCD is 16. Rename using the LCD. Answer: Subtract the numerators.

108 Find. Write the mixed numbers as improper fractions. Rename the fractions using the LCD. Simplify. Answer: Subtract.

110 Jogging Juyong jogged three days this week. She jogged miles, miles, and miles. How far did she jog altogether? Explore You know the distances Juyong jogged each day. Plan Add the daily distances together to find the total distance. Estimate your answer.

111 Solve Rename the fractions with LCD, 20. Add the like fractions. Answer: Juyong jogged miles. Examine Since is close to, the answer is reasonable.

112 Gardening Howard s tomato plants grew inches during the first week after sprouting, inches during the second week, and inches the third week. Find the total growth during the first three weeks after sprouting. Answer: inches

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114 Click the mouse button or press the Space Bar to display the answers.

115 Example 1 Find the Mean, Median, and Mode Example 2 Use a Line Plot Example 3 Find Extreme Values that Affect the Mean Example 4 Use, Mean, Median, and Mode to Analyze Data Example 5 Work Backward

116 Movies The revenue of the 10 highest grossing movies as of June 2000 are given in the table. Find the mean, median, and mode of the revenues. Top 10 Movie Revenues (millions of \$) Answer: The mean revenue is \$379.8 million.

117 To find the median, order the numbers from least to greatest. 290, 306, 309, 313, 330, 357, 400, 431, 461, 601 Answer: The median revenue is \$343.5 million. There is an even number of items. Find the mean of the two middle numbers. Answer: There is no mode because each number in the set occurs once.

118 Test Scores The test scores for a class of nine students are 85, 93, 78, 99, 62, 83, 90, 75, 85. Find the mean, median, and mode of the test scores. Answer: mean, 83.3; median, 85; mode, 85

119 Olympics The line plot below shows the number of gold medals earned by each country that participated in the 1998 Winter Olympic games in Nagano, Japan. Find the mean, median, and mode for the gold medals won. Answer: The mean is

120 There are 24 numbers. The median number is the average of the 12 th and 13 th numbers. Answer: The median is 2. The number 0 occurs most frequently in the set of data. Answer: The mode is 0.

121 Families A survey of school-age children shows the family sizes displayed in the line plot below. Find the mean, median, and mode. Answer: mean, 4.3; median, 5; mode, 5

122 Quiz scores The quiz scores for a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an extreme value and describe how it affects the mean. The data value 0 appears to be an extreme value. Calculate the mean with and without the extreme value to find how it affects the mean. mean with extreme value mean without extreme value Answer: The extreme value 0 decreases the mean by or about 0.7.

123 Birth Weight The birth weights of ten newborn babies are given in pounds: 7.3, 8.4, 9.1, 7.9, 8.8, 6.5, 7.9, 4.1, 8.0, 7.5. Identify an extreme value and describe how it affects the mean. Answer: 4.1; it decreases the mean by about 0.4.

124 The table shows the monthly salaries of the employees at two bookstores. Find the mean, median, and mode for each set of data. Based on the averages, which bookstore pays its employees better? Bob s Books The Reading Place Bob s Books mean: median: 1290, 1400, 1400, 1600, 3650 median mode: \$1400

125 Bob s Books The Reading Place The Reading Place mean: median: 1400, 1450, 1550, 1600, 2000 median mode: none Answer: The \$3650 salary at Bob s Books is an extreme value that increases the mean salary. The employees at The Reading Place are generally better paid as shown by the median.

126 The number of hours spent exercising each week by men and women are given in the table. Find the mean, median, and mode for each set of data. Based on the averages, which gender exercises more? Men Women Answer: Men: mean, 5.7; median, 4.5; mode, none Women: mean, 3.7; median, 3; mode, 1 Men seem to exercise more.

127 Grid In Test Item Jenny s bowling average is 146. Today she bowled 138, 140, and 145. What does she need to score on her fourth game to maintain her average? Read the Test Item Find the sum of the first three games. Then write an equation to find the score needed on the fourth game.

128 Solve the Test Item Step 1 Find the sum of the first three games x. mean of the first three scores sum of first three scores Multiply each side by 3. Simplify.

129 Step 2 Find the fourth score, x. mean Write an equation. Substitution. Multiply each side by 4 and simplify. Subtract 423 from each side and simplify.

130 Answer: Jenny needs to score at least 161 to maintain her average of 146.

131 Emily scored 73, 82, and 85 on her first three math tests. What score does Emily need on the fourth test to give her an average of 82 for the four tests? Answer: 88

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133 Click the mouse button or press the Space Bar to display the answers.

134 Example 1 Solve by Using Addition Example 2 Solve by Using Subtraction Example 3 Solve by Using Division Example 4 Solve by Using Multiplication

135 Solve. Check your solution. Write the equation. Add to each side. Simplify. Rename the fractions using the LCD and add.

136 Answer: Simplify. Check Write the original equation. Replace y with. Simplify.

138 Solve. Check your solution. Write the equation. Subtract 8.6 from each side. Answer: Check: Simplify. Write the original equation. Replace m with 2.6. Simplify.

140 Solve. Check your solution. Write the equation. Divide each side by 9. Answer: Check: Simplify. Write the original equation. Replace a with 0.4. Simplify.

142 Solve. Check your solution. Write the equation. Multiply each side by 6. Answer: Simplify.

143 Check: Write the original equation. Replace x with 48. Simplify.

144 Solve. Check your solution. Write the equation. Multiply each side by. Answer: Simplify. Check the solution.

145 Check: Write the original equation. Replace t with 10. Simplify.

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148 Click the mouse button or press the Space Bar to display the answers.

149 Example 1 Identify an Arithmetic Sequence Example 2 Identify an Arithmetic Sequence Example 3 Identify Geometric Sequences

150 State whether the sequence 5, 1, 3, 7, 11,... is arithmetic. If it is, state the common difference and write the next three terms. 5, 1, 3, 7, 11 Notice that, and so on. Answer: The terms have a common difference of, so the sequence is arithmetic. Continue the pattern to find the next three terms.

151 11, 15, 19, 23 Answer: The next three terms of the sequence are 15, 19, and 23.

152 State whether the sequence 12, 7, 2, 3, 8,... is arithmetic. If it is, state the common difference and write the next three terms. Answer: arithmetic; 5; 13, 18, 23

153 State whether the sequence 0, 2, 6, 12, 20,... is arithmetic. If it is, state the common difference and write the next three terms. 0, 2, 6, 12, 20 The terms do not have a common difference. Answer: The sequence is not arithmetic. However, if the pattern continues, the next three differences will be 10, 12, and 14.

154 20, 30, 42, 56 The next three terms are 30, 42, and 56.

155 State whether the sequence 20, 17, 11, 2, 10,... is arithmetic. If it is, state the common difference and write the next three terms. Answer: not arithmetic

156 State whether the sequence 2, 4, 4, 8, 8, 16, is geometric. If it is, state the common ratio and write the next three terms. 2, 4, 4, 8, 8, 16, 16 Answer: There is no common ratio. The sequence is not geometric.

157 State whether the sequence 27, 9, 3, 1, 27, 9, 3, 1,,... is geometric. If it is, state the common ratio and write the next three terms. Answer: The common ratio is, so the sequence is geometric. Continue the pattern to find the next three terms.

158 ,,, The next three terms are,, and.

159 a. State whether the sequence 2, 8, 32, 128, 512,... is geometric. If it is, state the common ratio and write the next three terms. Answer: geometric; 4; 2048, 8192, 32,768 b. State whether the sequence 100, 20, 4,,... is geometric. If it is, state the common ratio and write the next three terms. Answer: geometric; ;,,

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161 Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Pre-Algebra Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to

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### Pre-Algebra Interactive Chalkboard Copyright by The McGraw-Hill Companies, Inc. Send all inquiries to:

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