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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
• http://www.algebralab.com/practice/practice.aspx?file=Algebra1_2-6.xml