Solved Examples and Worksheet for Interpreting Multiplication as Scaling or Resizing

Q1What is the relationship between the products 3142 × 825 and 3142 × 275?

A. Product of 3142 × 825 is half of the product of 3142 × 275.
B. Product of 3142 × 825 is thrice as large as the product of 3142 × 275.
C. Product of 3142 × 825 is twice as large as the product of 3142 × 275.
D. Product of 3142 × 825 is twice as large as the product of 3142 × 825.

Solutions
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Step: 1
Since 275 is 13 of 825 because 3 × 275 = 825.
Step: 2
That means 825 is 3 times as large as 275.
Step: 3
Therefore the product of 3142 × 825 will also be thrice as large as the product of 3142 × 275.
Correct Answer is :   Product of 3142 × 825 is thrice as large as the product of 3142 × 275.
Q2How does the product of 1265 × 130 compare to the product of 1265 × 650?

A. The product of 1265 × 650 is twice as large as the product of 1265 × 130.
B. The product of 1265 × 130 is equal to the product of 1265 × 650
C. The product of 1265 × 130 is half of the product of 1265 × 650
D. The product of 1265 × 130 is one-fifth of the product of 1265 × 650.

Solutions
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Step: 1
Since 130 is 15 of 650, because 5 × 130 = 650.
Step: 2
Therefore the product of 1265 × 130 will also be one-fifth of the product of 1265 × 650.
Correct Answer is :   The product of 1265 × 130 is one-fifth of the product of 1265 × 650.
Q3How does the product of 625 × 80 compare to the product of 625 × 40?

A. The product of 625 × 80 is half of the product of 625 × 40.
B. The product of 625 × 40 is 3 times less than the product of 625 × 80.
C. The product of 625 × 80 is twice as large as the product of 625 × 40.
D. The product of 625 × 80 is 3 times greater than the product of 625 × 40.

Solutions
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Step: 1
Since 40 is 12of 80, because 2 × 40 = 80.
Step: 2
That means, 80 is twice as large as 40.
Step: 3
Therefore the product of 625 × 80 will also be double or twice as large as the product of 625 × 40.
Correct Answer is :   The product of 625 × 80 is twice as large as the product of 625 × 40.
Q4What is the relationship between the products 438 × 250 and 438 × 125?

A. Product of 438 × 250 is thrice as large as the product of 438 × 125.
B. Product of 438 × 250 is twice as large as the product of 438 × 125.
C. Product of 438 × 250 is one-third of the product of 438 × 125.
D. Product of 438 × 250 is same as the product of 438 × 125.

Solutions
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Step: 1
Since 125 is 12 of 250 because 2 × 125 = 250.
Step: 2
That means, 250 is twice as large as 125.
Step: 3
Therefore the product of 438 × 250 is also twice as large as the product of 438 × 125.
Correct Answer is :   Product of 438 × 250 is twice as large as the product of 438 × 125.
Q5How does the product of 13 × 43 compare to the product of 39 × 43?
A. Product of 13 × 43 is same as the product of 39 × 43.
B. Product of 13 × 43 is twice as small as the product of 39 × 43.
C. Product of 13 × 43 is twice as large as the product of 39 × 43.
D. Product of 39 × 43 is thrice as large as the product of 13 × 43.

Solutions
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Step: 1
Since 13 is 13 of 39, because 3 × 13 = 39.
Step: 2
That means, 39 is 3 times as large as 13.
Step: 3
Therefore the product of 39 × 43 will also be thrice as large as the product of 13 × 43.
Correct Answer is :   Product of 39 × 43 is thrice as large as the product of 13 × 43.
Q6How is the product of 650 × 25 related to the product of 650 × 100?

A. Product of 650 × 25 is one-third of the product of 650 × 100.
B. Product of 650 × 25 is twice as large as the product of 650 × 100.
C. Product of 650 × 25 is one-fourth of the product of 650 × 100.
D. Product of 650 × 25 is half of the product of 650 × 100.

Solutions
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Step: 1
Since 25 is 14 of 100, because 4 × 25 = 100.
Step: 2
Therefore the product of 650 × 25 will also be one-fourth of the product of 650 × 100.
Correct Answer is :   Product of 650 × 25 is one-fourth of the product of 650 × 100.
Q7What is the relationship between the products 2000 × 60 and 2000 × 20?
A. Product of 2000 × 20 is thrice as large as the product of 2000 × 60.
B. Product of 2000 × 20 is twice as large as the product of 2000 × 60.
C. Product of 2000 × 20 is half of the product of 2000 × 60.
D. Product of 2000 × 60 is thrice as large as the product of 2000 × 20.

Solutions
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Step: 1
Since 20 is 13 of 60 because 20 × 3 = 60.
Step: 2
That means, 60 is 3 times as large as 20.
Step: 3
Therefore the product of 2000 × 60 will also be thrice as large as the product of 2000 × 20.
Correct Answer is :   Product of 2000 × 60 is thrice as large as the product of 2000 × 20.
Q8Ed has a bookstore and a flower shop of rectangular shape. Length and width of the flower shop are 50 yards and 12 yards respectively. Length and width of bookstore are 25 yards and 12 yards respectively. How do the area of flower shop compare to the area of bookstore?

A. Flower shop is twice as large as bookstore.
B. Flower shop is of the same area as bookstore.
C. There is no comparison between flower shop and bookstore.
D. Flower shop is half of the area of bookstore.

Solutions
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Step: 1
Length and width of the flower shop are 50 yards and 12 yards respectively.
  [Given.]
Step: 2
Length and width of bookstore are 25 yards and 12 yards respectively.
  [Given.]
Step: 3
So, the area (50 yards ×12 yards) of flower shop is twice as large as the area (25 yards × 12 yards) of bookstore.
Correct Answer is :   Flower shop is twice as large as bookstore.
Q9Henry has a bedroom that is 14 feet by 9 feet long. His brother, John has a bedroom that is 7 feet by 9 feet long. How do the dimensions and area of Henry's bedroom compare to his brother's bedroom?
A. The area of Henry′s bedroom is one-third of John′s bedroom.
B. Henry′s bedroom is twice as large as John′s bedroom.
C. Henry′s bedroom is twice as small as John′s bedroom.
D. The areas of both the bedrooms are equal

Solutions
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Step: 1
The area of Henry's bedroom is 14 feet × 9 feet.
  [Given.]
Step: 2
The area of John's bedroom is 7 feet × 9 feet.
  [Given.]
Step: 3
Since 12 of 14 = 7 because 2 × 7 =14.
  [Since length is same for both the rooms.]
Step: 4
That means, 14 feet is twice as large as 7 feet.
Step: 5
Therefore the area of Henry's bedroom (14 feet × 9 feet) will also be twice as large as the area (7 feet × 9 feet) of John's bedroom.
Correct Answer is :   Henry′s bedroom is twice as large as John′s bedroom.
Q10Jim wants to draw a picture of length 6 cm and width 9 cm. His friend Diana wants to draw a picture of length 6 cm and width 3 cm. How do the area of Jim's picture compare to the area of Diana's picture?

A. Jim′s picture is twice as large as Diana′s picture.
B. The areas of both the pictures are equal.
C. The area of Diana′s picture is one-third of Jim′s picture.
D. Jim′s picture is twice as small as Diana′s picture.

Solutions
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Step: 1
The area of Jim's picture is 6 cm × 9 cm.
  [Given.]
Step: 2
The area of Diana's picture is 6 cm × 3 cm.
  [Given.]
Step: 3
Since 13 of 9 = 3, because 3 × 3 = 9.
  [Since width is same for both the pieces.]
Step: 4
That means, 3 is one-third of 9.
Step: 5
Therefore the area of Diana's picture (6 cm × 3 cm) will also be one-third of the area (6 cm × 9 cm) of Jim's picture.
Correct Answer is :   The area of Diana′s picture is one-third of Jim′s picture.

HighSchool Math