Distributive Property:Advanced Problems

It may be necessary to review the basic distributive property

problems in the number property introduction PowerPoint

presentation

Recall the distributive property of multiplication over addition . . .

symbolically:

a × (b + c) = a × b + a × cand pictorially (rectangular array area model):

a × b a × ca

b c

An example: 6 x 13 using your mental math skills . . .

symbolically:

6 × (10 + 3) = 6 × 10 + 6 × 3and pictorially (rectangular array area model):

6 × 10 6 × 36

10 3

Find the area of the rectangle.Area = length x width

6 ft

24 ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

6 ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

6 ft

Find the area of each rectangle.

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

6 ft

Find the area of each rectangle.

6 x 20 = 120 sq ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

6 ft

Find the area of each rectangle.

6 x 20 = 120 sq ft 6 x 4 = 24

sq ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

6 ft

Find the area of each rectangle.

120 sq ft 24 sq ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

6 ft

Now put the two rectangles back together.

120 sq ft 24 sq ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

Now put the two rectangles back together.

120 sq ft 24 sq ft

Find the area of the rectangle.Area = length x width

6 ft

20 ft + 4 ft

Now put the two rectangles back together.

120 sq ft 24 sq ft

Find the area of the rectangle.Area = length x width

6 ft

24 ft

Now put the two rectangles back together.

120 sq ft

+ 24 sq ft

Find the area of the rectangle.Area = length x width

6 ft

24 ft

Now put the two rectangles back together.

144 sq ft

A swimming pool has a shallow end and a deep end. Find the surface

area of the pool.

shallow waterdeepwater8

yds

5 yds 10 yds

shallow waterdeepwater8

yds

5 yds 10 yds

8 yds

Break the pool into a deep end and a shallow end.

shallow waterdeepwater8

yds

5 yds 10 yds

8 yds

Find the area of the deep end.

shallow water8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the deep end.

shallow water8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the shallow end.

8 x 10 = 80

8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the shallow end.

8 x 10 = 80

8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Now sum the two areas together.

80 408 yds

5 yds 10 yds

Now sum the two areas together.

+

80 408 yds

5 yds 10 yds

40 + 80 = 120 square yards

Write an expression that shows how to find the area of the

rectangle and uses the distributive property.

9 yds

5 yds 20 yds

Find the areas for each individual rectangle.

9 yds

5 yds 20 yds

Find the areas for each individual rectangle.

9 yds

5 yds 20 yds

(9 x 5)

Find the areas for each individual rectangle.

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)

Sum the two areas.

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)+

(9 x 5) + (9 x 20) = area

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)

Practice Time

1) Which of the following expressions shows the distributive

property for 5 x (3 + 7)?

(5 x 3) + (5 x 7)

(5 x 3) x (5 x 7)

(5 + 3) x (5 + 7)

1) Which of the following expressions shows the

distributive property for 5 x (3 + 7)?

(5 x 3) + (5 x 7)

Correct!

2) Which of the following expressions shows the distributive

property for 3 x (9 + 4) ?

(3 x 9) + (3 x 4)

(3 + 9) + (3 + 4)

(3 + 9) x (3 + 4)

2) Which of the following expressions shows the

distributive property for 3 x (9 + 4) ?

(3 x 9) + (3 x 4)

Correct!

3) Which of the following expressions is equivalent to:

2 + 3 + 2 + 3 and shows the distributive property.

2 x (2 + 3)

2 + 2 + 3 + 3

3 x (2 + 3)

3) Which of the following expressions is equivalent to:

2 + 3 + 2 + 3 and uses the distributive

property.

2 x (2 + 3) Correct!

4) Which of the following expressions is equivalent to:

(4 x 3) + (4 x 8) ?

4 x (3 + 8)

8 x (3 + 4)

3 x (4 + 8)

4) Which of the following expressions is equivalent to:

(4 x 3) + (4 x 8) ?

4 x (3 + 8)

Correct!

5) Which of the following expressions is equivalent to:

(5 x 9) + (5 x 3) ?

9 x (3 + 5)

5 x (9 + 3)

3 x (9 + 5)

5) Which of the following expressions is equivalent to:

(5 x 9) + (5 x 3) ?

5 x (9 + 3) Correct!

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 yds

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 yds

4 x 3

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 yds

4 x 3 4 x 9

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 yds

4 x 3 4 x 9

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 x 3 4 x 9

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 x 3 4 x 9

6) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

4 yds

3 yds 9 yds

4 x 3 + 4 x 9

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 yds

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 yds

6 x 4

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 yds

6 x 4 6 x 8

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 yds

6 x 4 6 x 8

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 x 4 6 x 8

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 x 4 6 x 8

7) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

6 yds

4 yds 8 yds

6 x 4 + 6 x 8

8) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

5 yds

2 yds 10 yds

8) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

5 yds

2 yds 10 yds

5 x 2 5 x 10

8) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

5 yds

2 yds 10 yds

5 x 2 + 5 x 10

9) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

8 yds

3 yds 5 yds

9) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

8 yds

3 yds 5 yds

8 x 3 8 x 5

9) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

8 yds

3 yds 5 yds

8 x 3 + 8 x 5

10) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

5 yds

x yds 10 yds

10) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

5 yds

x yds 10 yds

5x 5 ∙ 10

10) Write an expression that shows how to find the area of the rectangle and uses

the distributive property.

5 yds

x yds 10 yds

5x + 5 ∙ 10

11) Which expression is equivalent to 3(x + 7)?

3x + 7

x + 21

x + 10

3x + 21

11) Which expression is equivalent to 3(x + 7)?

3x + 21 Correct!

12) Which expression is equivalent to 4(x + 5)?

4x + 5

4x + 20

x + 9

9x

12) Which expression is equivalent to 4(x + 5)?

4x + 20 Correct!

13) Which expression is equivalent to 8(x + 2)?

8x + 16

8x + 2

10x

8x + 10

13) Which expression is equivalent to 8(x + 2)?

8x + 16 Correct!

14) Which expression is equivalent to 2(x + 3)?

2x + 3

2x + 5

2x + 6

2x + 2

14) Which expression is equivalent to 2(x + 3)?

2x + 6 Correct!

Click below to see video

• http://www.youtube.com/watch?v=nVbRzhOIgm0

• http://glencoe.mcgraw-hill.com/sites/007888523x/student_view0/chapter4/lesson1/personal_tutor.html

• http://www.youtube.com/watch?v=itmz8i62Ag4

Click to Test Your Skills

• http://glencoe.mcgraw-hill.com/sites/007888523x/student_view0/chapter4/lesson1/self-check_quizzes.html

• http://www.algebrahelp.com/worksheets/view/simplifying/distribution.quiz

• http://algebralab.org/studyaids/studyaid.aspx?file=Algebra1_2-6.xml

• http://www.algebra-class.com/distributive-property-practice.html

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