Solved Examples and Worksheet for Multiplying Rational Numbers

Q1A square occupies 45 of a rectangle. The area of rectangle is 40 in.2. What is the area of the square?
A. 40 in.2
B. 50 in.2
C. 32 in.2
D. 72 in.2

Solutions
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Step: 1
The area of the square = Fraction of the rectangle occupied by the square × Area of the rectangle
Step: 2
= 45 × 40
  
Step: 3
= (4 × 8)
  [Dividing numerator and denominator by their GCF.]
Step: 4
= 32 in.2
  [Simplify.]
Correct Answer is :   32 in.2
Q2Find the product of (- 25) and (- 20).

A. 12
B. - 8
C. 10
D. 8

Solutions
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Step: 1
(- 25) × (- 20) = - 2×(- 20)5
  [Since ( ab) × c = a×cb .]
Step: 2
= - 2×(- 4)1
  [Divide the numerator and the denominator by their GCF, 5.]
Step: 3
= 8
  [Simplify the numerator.]
Step: 4
The product (- 25) and (- 20) is 8.
Correct Answer is :   8
Q3Find the product of - 112 and (- 134).
A. - 76
B. - 2113
C. - 2116
D. 218

Solutions
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Step: 1
- 112 × (- 134)
  [Original fractions.]
Step: 2
= - 32 × - 74
  [Rewrite the mixed numbers as improper fractions.]
Step: 3
= - 3× - 72×4
  [Since ( ab) × ( cd) = a×cb×d.]
Step: 4
The product of - 112 and (- 134) is 218.
Correct Answer is :   218
Q4Find the product. 49 × - 416
A. - 16
B. 122512
C. - 12256
D. - 122518

Solutions
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Step: 1
49 × - 416
  [Original expression.]
Step: 2
= 491 × - 256
  [Rewrite the number 49 as a fraction and the mixed number - 416 as an improper fraction.]
Step: 3
= (49)(- 25)(1)(6)
  [Since ab × cd = acbd.]
Step: 4
= - 12256
  [Find the products.]
Step: 5
The product of 49 and - 416 is - 12256.
Correct Answer is :   - 12256
Q5Find the product of (- 25) and (- 30).
A. 12
B. 16
C. - 12
D. 14

Solutions
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Step: 1
(- 25) × (- 30) = (- 2) × (- 30)5
  [Since (ab) × c = a × cb.]
Step: 2
= - 2 × (- 6)1
  [Divide the numerator and the denominator by their GCF, 5.]
Step: 3
= 12
  [Simplify the denominator.]
Step: 4
The product of (- 25) and (- 30) is 12.
Correct Answer is :   12
Q6Find the product of 645 and 789.

A. 80315
B. 2414135
C. 241445
D. 120745

Solutions
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Step: 1
645 × 789
  [Original expression.]
Step: 2
= 345 × 719
  [Rewrite the mixed numbers as improper fractions.]
Step: 3
= (34)(71)(5)(9)
  [ab × cd = acbd.]
Step: 4
= 241445
  [Simplify the numerator and denominator.]
Step: 5
The product of 645 and 789 is 241445.
Correct Answer is :   241445
Q7Find the product of (- 112) and (- 134).

A. - 2116
B. 218
C. - 76
D. 2113

Solutions
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Step: 1
- 112 × (- 134)
  [Original fractions.]
Step: 2
= - 32 × - 74
  [Rewrite the mixed numbers as improper fractions.]
Step: 3
= (- 3) × (- 7)2 × 4
  [Since (ab) × (cd) = a × cb × d .]
Step: 4
= 218
  [Multiply inside the grouping symbols.]
Step: 5
The product of (- 112) and (- 134) is 218.
Correct Answer is :   218
Q8Find the area of a rectangle whose length is 57 cm and width is 611 cm ?

A. 3077 sq.cm
B. 7730 sq.cm
C. 4255 sq.cm
D. 5542 sq.cm

Solutions
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Step: 1
The area of a rectangle = length × width
  [Formula.]
Step: 2
The area of the rectangle = 57 × 611
  [Substitute length = 57 cm and widtgh = 611 cm.]
Step: 3
= 5 × 67 × 11
  [Since, ab × cd = a × cb × d.]
Step: 4
= 3077
Step: 5
Therefore, the area of the rectangle is 3077 sq.cm
Correct Answer is :   3077 sq.cm

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