Homework 13-7
Name
Area and the
Distributive Property
Another Look!
You can use the Distributive Property to break apart
multiplication facts to find the product.
You can separate a rectangle into two
smaller rectangles with the same total area.
You can write the
multiplication fact that
represents the area of
the large rectangle.
5
4
You can write the
multiplication facts that
represent the area of each
of the smaller rectangles.
5
3
2
4
4 × 5 = 20
4 × 5 = 4 × (3 + 2)
4 × 5 = (4 × 3) + (4 × 2)
4 × 5 = 12 + 8 = 20
In 1 through 4, write the equation that represents the picture.
1.
5
3
3
2.
3.
4.
2
□ = □ × (3 + □)
3 × □ = (3 × □) + (□ × 2)
3 × □ = □ + □ = 15
□ × 7 = □ × (□ + 4)
□ × 7 = (□ × 3) + (4 × □)
□ × 7 = □ + □ = 28
3×
The areas of the large
rectangles are equal to
the sum of the areas of
the smaller rectangles.
□ = □ × (2 + □)
3 × □ = (3 × □) + (□ × 4)
3 × □ = □ + □ = 18
□ × 6 = □ × (□ + 3)
□ × 6 = (□ × 3) + (5 × □)
□ × 6 = □ + □ = 30
3×
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Topic 13 Lesson 13-7
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5. Communicate Tina divided the rectangle
below into two smaller parts. Show
another way to divide the rectangle into
two smaller parts. Write the number
sentence you could use to find the area
of the two smaller rectangles.
6. Number Sense The tallest skyscraper in
Texas has a height of 1,002 feet. What is
this number in expanded form? in word
form?
7. Which equation represents the picture?
A 3 × 10 = 3 × (3 + 6) = (3 × 3) + (3 × 6)
B 3 × 9 = 3 × (4 + 5) = (3 × 4) + (3 × 5)
C 3 × 9 = 3 × (3 + 6) = (3 × 3) + (3 × 6)
D 3 × 9 = 3 × (2 + 7) = (3 × 2) + (3 × 7)
8. Reason Lee wants to cut a 3 × 6 piece
of canvas into two rectangles that are
3 × 2 and 3 × 5. He wants the sum of
the areas of the two small rectangles
to be the same as the area of the large
rectangle. Can Lee do this? Explain.
9. Extend Your Thinking George divided a
rectangular sheet of stickers into
6 rows of 5 and 6 rows of 3. How were
the stickers arranged before George
separated them into two smaller
rectangles? Write a number sentence
to justify your answer.
10. Communicate Darren has a piece of
wood that is 7 inches by 8 inches. Explain
how he could divide this large rectangle
into two smaller rectangles.
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