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 × c and pictorially (rectangular array area model): a × ba × ca bc

An example: 6 x 13 using your mental math skills... symbolically: 6 × (10 + 3) = 6 × × 3 and pictorially (rectangular array area model): 6 × 106 ×

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 water deepw ater 8 yds 5 yds 10 yds

shallow water deepw ater 8 yds 5 yds 10 yds 8 yds Break the pool into a deep end and a shallow end.

shallow water deepw ater 8 yds 5 yds 10 yds 8 yds Find the area of the deep end.

shallow water 8 x 5 = 40 8 yds 5 yds 10 yds 8 yds Find the area of the deep end.

shallow water 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 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.

yds 5 yds 10 yds Now sum the two areas together. +

yds 5 yds 10 yds = 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: and shows the distributive property. 2 x (2 + 3) x (2 + 3)

3) Which of the following expressions is equivalent to: 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 yd s

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 yd s 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 yd s 4 x 34 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 yd s 4 x 34 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 34 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 34 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 46 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 46 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 46 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 46 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 25 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 38 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 5x5 ∙ 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 x + 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 + 20Correct!

13) Which expression is equivalent to 8(x + 2)? 8x x x 8x + 10

13) Which expression is equivalent to 8(x + 2)? 8x + 16Correct!

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!

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