3-3 Multiplying Rational Numbers

Find each product. Write in simplest form.

SOLUTION:

ALGEBRA Evaluate each expression if x = , y = , and z = . Write the product in simplest

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

13. GEOGRAPHY “Midway” is the name of 252 towns in the United States. “Pleasant Hill” occurs as many times.

How many towns named “Pleasant Hill” are there in the United States?

SOLUTION:

There are 140 towns in the United States named “ Pleasant Hill.”

14. SCHOOL SPORTS Of the 480 students at Pleasantview Middle School, play a school sport. How many

students play a sport?

SOLUTION:

Pleasantville Middle School has 312 students who play a school sport.

SOLUTION:

ALGEBRA Evaluate each expression if a = , b = , and c = . Write the product in simplest

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

33. BEEF The average person living in Argentina consumes about 145 pounds of beef per year. The average person

living in the United States consumes about as much. How many pounds of beef does the average American

consume every year?

SOLUTION:

The average American consumes 87 pounds of beef each year.

34. BRIDGES The Golden Gate Bridge in San Francisco is 4200 feet long. The Brooklyn Bridge in New York City is

as long. How long is the Brooklyn Bridge?

SOLUTION:

The Brooklyn Bridge is 1596 feet long.

SOLUTION:

41. LAWN CARE Dexter’s lawn is of an acre. If bags of fertilizer are needed for 1 acre, how much will he

need to fertilize his lawn?

SOLUTION:

Dexter will need 5 bags of fertilizer for his lawn.

42. HYBRID CARS A certain hybrid car can travel times as far as a similar nonhybrid car with one gallon of

gasoline. If the nonhybrid car can travel 33 miles per gallon of gasoline, how far can the hybrid travel on gallon of

gasoline?

SOLUTION:

The hybrid car can travel 36 miles on gallon of gasoline.

MEASUREMENT Complete.

43. _ ounces = pound

(Hint: 1 pound = 16 ounces)

SOLUTION:

12 ounces = pound

44. _ feet = mile

(Hint: 1 mile = 5280 feet)

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

46. minute = _ seconds

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

(Hint: 1 gallon = 16 cups)

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

49. RESEARCH Use a cookbook to find a recipe for guacamole. Change the recipe to make times the original

amount.

SOLUTION: Sample answer: Recipe for guacamole 3 avacados 1 tomato

cup finely diced onion

1 Tablespoon fresh lemon juice salt to taste

To make times the original amount, you will need:

and salt to taste.

50. ANALYZE TABLES Use the table that shows statistics from the last election for 8th grade class president. There are 540 students in the 8th grade.

a. How many students voted for Hector? b. How many students voted for Nora? c. Were there other candidates for class president? How do you know? Explain your reasoning. If there were other candidates, what fraction of the student body voted for them?

SOLUTION: a.

243 students voted for Hector. b.

135 students voted for Nora.

c. Yes. A third candidate, or a combination of other candidates, must have received votes. If of the class voted,

then or 405 students voted. Hector and Nora received a total of 243 + 135 or 378 votes. Subtracting 378

from 405 leaves 27 votes not shown in the table. So, or of the student body voted for the other candidate

51. NUMBER SENSE The expression × 4 means of 4. The number line shows that the product of and 4 is 2.

Find each product using a number line.

a. of 6

b. of 8

d. of 2

g. Look back at the solutions for Exercises d–f. What pattern do you notice?

h. What is the product of where a, b ≠ 0?

SOLUTION: a.

g. Each product is 1.

52. OPEN ENDED Find two rational numbers greater than whose product is less than .

SOLUTION:

Sample answer: and are both greater than .

53. ERROR ANALYSIS Kelly and Marina are finding . Is either of them correct? Explain your reasoning.

SOLUTION:

Marina is correct. Kelly did not write the mixed numbers as improper fractions before multiplying.

CHALLENGE Find each missing fraction.

SOLUTION: Divide the quotient by the given factor to find the missing factor. When dividing by a fraction, you multiply by the reciprocal.

57. REASONING Investigate the product of a fraction between 0 and 1 and a whole number or mixed number. Is the product always, sometimes, or never less than the whole number or mixed number? Explain.

SOLUTION: The product of a fraction between 0 and 1 and a whole number or mixed number is always less than the whole number. Sample answer: When you multiply a fraction by a whole number or mixed number, you are finding a part of that whole number or mixed number. Since you are finding a part, the product will always be less than the whole number or mixed number.

58. WRITING IN MATH Estimate . Then find the actual product. Explain why the estimate and the product

are different. What could you do to make your estimate closer to the actual product?

SOLUTION: Estimate: 4 × 5 = 20 Actual:

The estimated and actual products are different because both fractional parts were slightly greater than one-half, butboth were rounded up. If you have mixed numbers and both are rounded up, your estimate may be closer to the actual product if you round one mixed number up and the other one down.

59. Of the students in Mr. Boggs’ class, participate in an after school sport. Of these, participate in track and

field. What fraction of the students participates in track and field?

SOLUTION:

of the students participate in track and field. Choice A is correct.

60. Which statement is shown on the number line below?

SOLUTION:

The number line shows seven increments of , or . The result is . Choice G is correct.

61. What is the value of the expression 2ab if a = and b = ?

SOLUTION:

Choice B is correct.

62. EXTENDED RESPONSE The length of one side of a square garden tile is feet.

a. Write a mixed number to represent the perimeter of the tile. b. Write a mixed number to represent the area of the tile. c. What is the perimeter of the tile in inches? d. What is the area of the tile in square inches?

SOLUTION: a. A square has four sides of equal length, so multiply the side length by 4 to find the perimeter.

The perimeter of the tile is feet.

b. The area of a square is equal to the side length squared.

The area of the tile is ft².

c. There are 12 inches in a foot.

The perimeter of the tile is 80 inches. d. There are 144 square inches in a square foot.

The perimeter of the tile is 400 in.².

Write each decimal as a fraction or mixed number in simplest form.63. 4.02

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

SOLUTION: Let N represent the number.

So, = .

Replace each _ with <, >, or = to make a true sentence.

69. 0.3 _

SOLUTION:

Write as a decimal and then compare the decimals.

Since 0.3 is to the right of 0.25 on a number line, .

70. _ 0.65

SOLUTION:

Since 0.625 is to the left of 0.65 on a number line, .

71. _ 0.4

SOLUTION:

Since both values are equal to 0.4, .

SOLUTION: Write the fractions as decimals and then compare the decimals.

Since 0.875 is to the left of on a number line, .

SOLUTION:

Since both values are equal to , .

75. SLEEP In an online survey, about of teenagers go to sleep between 9 and 10 P.M., while of teenagers go to

sleep at 12 A.M. or later. Which group is larger?

Because 0.25 < 0.26, . The group that goes to sleep at 12 A.M. or later is larger.

Find each product.76. 14(–5)

SOLUTION: The product of two integers with different signs is negative. So, 14(–5) = –70.

77. –8(–11)

SOLUTION: The product of two integers with the same sign is positive. So, –8(–11) = 88.

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

Multiply.80. –50(–5)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

eSolutions Manual - Powered by Cognero Page 1

3-3 Multiplying Rational Numbers

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

form. 7. xy

SOLUTION:

11. 4y

SOLUTION:

form. 27. bc

SOLUTION:

28. ab

SOLUTION:

29. 2c

SOLUTION:

31. –4bc

SOLUTION:

consume every year?

SOLUTION:

gasoline?

SOLUTION:

12 ounces = pound

44. _ feet = mile

SOLUTION:

3520 feet = mile

45. foot = _ inches

SOLUTION:

foot = 10 inches

SOLUTION:

minute = 15 seconds

47. _ cups = gallon

SOLUTION:

4 cups = gallon

48. year = _ weeks

SOLUTION:

year = 39 weeks

amount.

and salt to taste.

SOLUTION: a.

a. of 6

b. of 8

d. of 2

SOLUTION: a.

SOLUTION:

64. 0.215

SOLUTION:

65. –5.125

SOLUTION:

So, = .

69. 0.3 _

SOLUTION:

70. _ 0.65

SOLUTION:

71. _ 0.4

SOLUTION:

77. –8(–11)

78. –7(–8)(–3)

SOLUTION:

79. 2(–8)(–9)(10)

SOLUTION:

81. (12)(–2)(8)

SOLUTION:

82. (–1)(16)(–2)

SOLUTION:

83. 14(–2)(–3)

SOLUTION:

3-3 Multiplying Rational Numbers

Documents

Transcript of 3-3 Multiplying Rational Numbers