Solved Examples and Worksheet for Multiplying Rational Numbers

Q1What is the value of
- 49 × 9 × - 13?
A. 5733
B. 4212
C. - 5733
D. - 4212

Solutions
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Step: 1
- 49 × 9 × - 13
  [Original expression.]
Step: 2
= - 441 × - 13
  [The product of two integers with opposite signs is negative.]
Step: 3
= 5733
  [The product of two integers with same sign is positive.]
Correct Answer is :   5733
Q2Find 56 of 67 .
A. 142
B. 3143
C. 3536
D. 57

Solutions
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Step: 1
56 of 67 = 56 × 67
  [Original expression.]
Step: 2
= 5 × 66 × 7 = 3042
  [Multiply numerators and denominators separately.]
Step: 3
= 57
  [Simplify using the GCF 6.]
Step: 4
56 of 67 is 57 .
Correct Answer is :   57
Q3Find the product of 56 and 65 .
A. 12
B. 0
C. 1
D. 14

Solutions
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Step: 1
56 × 65
  [Product of 56 and 65.]
Step: 2
= 5 × 66 × 5
  [Multiply numerators and denominators separately.]
Step: 3
= 3030 = 1
  [Simplify.]
Correct Answer is :   1
Q4Apple juice requires 56 of a cup of water and juice concentrate of 145 of the water quantity. How much juice concentrate is required for the apple juice?

A. 155 cup
B. 153 cup
C. 154 cup
D. None of the above

Solutions
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Step: 1
= 145 × 56
  [Original expression.]
Step: 2
= 19 × 16
  [Cancel 45 with 5.]
Step: 3
= 1×19×6 = 154
  [Multiply numerators and denominators separately.]
Step: 4
The apple juice requires 154 cup of juice concentrate.
Correct Answer is :   154 cup
Q5Find the product of 98 and 107.
A. 11119
B. 11728
C. 158
D. 13457

Solutions
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Step: 1
= 98 × 107
  [Original expression.]
Step: 2
= 9 × 108 × 7
  [Multiply the numerators and denominators.]
Step: 3
= 9056
  [Simplify.]
Step: 4
= 4528
  [Divide numerator and denominator by their GCF 2.]
Step: 5
= 11728
  [Write as a mixed fraction.]
Correct Answer is :   11728
Q6Find the product of 129 and 45 .

A. 4445
B. 1514
C. 845
D. 11936

Solutions
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Step: 1
129 × 45
  [Original expression.]
Step: 2
= 119 × 45
  [Convert mixed number into improper fraction.]
Step: 3
= 11 × 49 × 5
  [Multiply the numerators and the denominators.]
Step: 4
= 4445
  
Step: 5
The product of 129 and 45 is 4445.
Correct Answer is :   4445
Q7Find the product of 49 and 19.

A. 1049
B. 949
C. 749
D. 849

Solutions
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Step: 1
49 × 19
  [Original expression.]
Step: 2
= 49 × 191
  [Write 19 as 191.]
Step: 3
= 4 × 199 × 1
  [Multiply the numerators and the denominators.]
Step: 4
= 769
  
Step: 5
= 849
  [Convert improper fraction into mixed number.]
Step: 6
The product of 49 and 19 is 849.
Correct Answer is :   849
Q8Find the product of 28 and 337.

A. 4483
B. 120
C. 36
D. 96

Solutions
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Step: 1
28 × 337
  [Original expression.]
Step: 2
= 281 × 247
  [Write the mixed number as the improper fraction and 28 as 281.]
Step: 3
= 28 × 241 × 7
  [Multiply the numerators and the denominators.]
Step: 4
= 6727
  [Simplify.]
Step: 5
= 961 = 96
  [Write 961 as 96.]
Correct Answer is :   96
Q9Henry ate 47 of a pizza and Valerie ate 14 of what Henry ate. How much did Valerie eat?

A. 17
B. 14
C. 47
D. None of the above

Solutions
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Step: 1
14 × 47
  [Original expression.]
Step: 2
= 11 × 17
  [Divide by the GCF 4.]
Step: 3
= 1×11×7
  [Multiply the numerators and the denominators.]
Step: 4
= 17
  
Step: 5
Valerie ate 17 of the pizza.
Correct Answer is :   17
Q10Tim bought 3812 inches of rope and used 27 of it. How much rope did he use?

A. 13 in.
B. 10 in.
C. 12 in.
D. 11 in.

Solutions
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Step: 1
27 × 3812
  [Original expression.]
Step: 2
= 27 × 772
  [Write the mixed number as an improper fraction.]
Step: 3
= 11 × 111
  [Cancel 2 with 2 and 77 with 7.]
Step: 4
= 1 × 111 × 1
  [Multiply the numerators and the denominators.]
Step: 5
= 111 = 11
  [Write 111 as 11.]
Step: 6
Tim used 11 in. of the rope.
Correct Answer is :   11 in.
Q11Justin's bag contains popcorns weighing 14 oz. Edward's bag contains 13 of Justin's bag of popcorns. Calculate the weight of popcorns in Edward's bag.
A. 34 oz.
B. 113 oz.
C. 111 oz.
D. 112 oz.

Solutions
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Step: 1
The weight of Edward's bag of popcorns = (14 × 13) oz.
Step: 2
= 1×14×3 oz.
  [Multiply numerators and denominators.]
Step: 3
= 112 oz.
  [Simplify.]
Step: 4
Edward's bag contains popcorns weighing 112 oz.
Correct Answer is :   112 oz.
Q12Ed wants to paint a rectangular wall. The length and the width of the wall are 715 ft and 556 ft respectively. Find the area of the wall Ed has to paint.

A. 43 ft2
B. 42 ft2
C. 41 ft2
D. 44 ft2

Solutions
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Step: 1
The area of the rectangular wall = length × width
Step: 2
= 715 × 556
  
Step: 3
= 365 × 356
  [Write each mixed number as an improper fraction.]
Step: 4
= 61 × 71
  [Cancel 36 with 6 and 35 with 5.]
Step: 5
= 6 × 71 × 1
  [Multiply numerators and denominators.]
Step: 6
= 421 = 42
  [Write 421 as 42.]
Step: 7
The area of the wall Ed has to paint is 42 ft2.
Correct Answer is :   42 ft2
Q13A truck travels 50 mi in one hour. What is the distance traveled by the truck in 5 hours?
A. 255 mi
B. 260 mi
C. 280 mi
D. 250 mi

Solutions
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Step: 1
Distance traveled by the truck in 5 hours = (Distance traveled in 1 hour) × 5
Step: 2
= 50 × 5
  [Substitute the values.]
Step: 3
As multiplication is nothing but repeated addition, add 50 to itself 5 times.
Step: 4
50 × 5 = 250
  [Multiply.]
Step: 5
The truck travels 250 mi in 5 hours.
Correct Answer is :   250 mi
Q14Compute:
- 5 × 3(- 5)
A. - 75
B. 75
C. 80
D. - 80

Solutions
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Step: 1
- 5 × 3(- 5)
  [Original expression.]
Step: 2
- 5 × 3(- 5) = - 5 × - 15
  [The product of a negative integer and a positive integer is negative.]
Step: 3
= 75
  [Multiply. The product of two negative integers is positive.]
Step: 4
The product of - 5 × 3(- 5) is 75.
Correct Answer is :   75
Q15Compute.
- 7 × - 4(- 3)

A. - 84
B. 94
C. - 94
D. 84

Solutions
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Step: 1
- 7 × - 4(- 3)
  [Original expression.]
Step: 2
- 7 × - 4(- 3) = - 7 × 12
  [The product of two negative integers is positive.]
Step: 3
= - 84
  [Multiply. The product of a negative integer and a positive integer is negative.]
Step: 4
The product of - 7 × - 4(- 3) is - 84.
Correct Answer is :   - 84

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