# distributive property: advanced problems

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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 c - PowerPoint PPT PresentationTRANSCRIPT

Distributive Property:Advanced ProblemsIt 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 ba cabc

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

6 (10 + 3) = 6 10 + 6 3and pictorially (rectangular array area model):6 106 36103

Example 1-1aAnswer:52

Example 1-1bAnswer:30

Example 1-1c

Example 1-2aReal Life Example: Recreation North Country Rivers of York, Maine, offers one-day white-water rafting trips on the Kennebec River. The trip costs $69 per person, and wet suits are $15 each.Write two equivalent expressions to find the total cost of one trip for a family of four if each person uses a wet suit.Method 1 Find the cost for 1 person, then multiply by 4.

Example 1-2aMethod 2Find the cost of 4 trips and 4 wet suits. Then add.

Example 1-2bEvaluate either expression to find the total cost.Answer:The total cost is $336.CheckYou can check your results by evaluating 4($84).

Example 1-2cMovies The cost of a movie ticket is $7 and the cost of a box of popcorn is $2. a.Write two equivalent expressions to find the total cost for a family of five to go to the movies if each member of the family gets a box of popcorn. b.Find the total cost. Answer:$45

Example 1-3a

Example 1-3b

Example 1-3c

Example 1-4a

Example 1-4b

Example 1-4c

Real-Life Example 2Mental Math

The distributive property is mental math strategy that can be used when multiplying.43 x 5 =?

Break apart the double-digit number.43 x 5 =? 40 3+

Then multiply each part by 5.43 x 5 =? 40 3 x 5 x 5+

Then multiply each part by 5.43 x 5 =? 40 3 x 5 x 5 200 15+

Finally, sum your two products43 x 5 =215 40 3 x 5 x 5 200 15+= 215+

Lets look at another example.53 x 6 = ?

Break apart the double-digit number.53 x 6 = ?

Break apart the double-digit number.53 x 6 = ?50 3+

Multiply each part by 6.53 x 6 = ?50 3 x 6 x 6+

Multiply each part by 6.53 x 6 = ?50 3 x 6 x 6 300 18+

Sum the two products.53 x 6 = 31850 3 x 6 x 6 300 + 18 = 318+

The word distribute means to give out.

Distribute the cubes to the girls.

Distribute the cubes to the girls.

Distribute the cubes to the girls.

Distribute the cubes to the girls.

Distribute the cubes to the girls.

Distribute the cubes to the girls.

In this example, the 5 was distributed.5 x 38 = 5 x (30 + 8) = (5 x 30) + (5 x 8)

In this example, the 7 was distributed.7 x 46 = 7 x (40 + 6) = (7 x 40) + (7 x 6)

Find the area of the rectangle.Area = length x width6 ft24 ft

Find the area of the rectangle. Area = length x width6 ft24 ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft6 ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft6 ftFind the area of each rectangle.

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft6 ftFind the area of each rectangle.6 x 20 = 120 sq ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft6 ftFind the area of each rectangle.6 x 20 = 120 sq ft6 x 4 = 24 sq ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft6 ftFind the area of each rectangle.120 sq ft24 sq ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ft6 ftNow put the two rectangles back together.120 sq ft24 sq ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ftNow put the two rectangles back together.120 sq ft24 sq ft

Find the area of the rectangle. Area = length x width6 ft20 ft+ 4 ftNow put the two rectangles back together.120 sq ft24 sq ft

Find the area of the rectangle. Area = length x width6 ft24 ftNow put the two rectangles back together.120 sq ft + 24 sq ft

Find the area of the rectangle. Area = length x width6 ft24 ftNow 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 yds5 yds 10 yds

shallow waterdeepwater8 yds5 yds 10 yds8 ydsBreak the pool into a deep end and a shallow end.

shallow waterdeepwater8 yds5 yds 10 yds8 ydsFind the area of the deep end.

shallow water8 x 5 = 408 yds5 yds 10 yds8 ydsFind the area of the deep end.

shallow water8 x 5 = 408 yds5 yds 10 yds8 ydsFind the area of the shallow end.

8 x 10 = 808 x 5 = 408 yds5 yds 10 yds8 ydsFind the area of the shallow end.

8 x 10 = 808 x 5 = 408 yds5 yds 10 yds8 ydsNow sum the two areas together.

80 408 yds5 yds 10 ydsNow sum the two areas together.+

80 408 yds5 yds 10 yds40 + 80 = 120 square yards

Write an expression that shows how to find the area of the rectangle and uses the distributive property.9 yds5 yds 20 yds

Find the areas for each individual rectangle.9 yds5 yds 20 yds

Find the areas for each individual rectangle.9 yds5 yds 20 yds(9 x 5)

Find the areas for each individual rectangle.9 yds5 yds 20 yds(9 x 5)(9 x 20)

Sum the two areas.9 yds5 yds 20 yds(9 x 5)(9 x 20)+

(9 x 5) + (9 x 20) = area9 yds5 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 + 33 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 yds3 yds 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 yds

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 yds4 x 3

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 yds4 x 34 x 9

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 yds4 x 34 x 9

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 x 34 x 9

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 x 34 x 9

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property.4 yds3 yds 9 yds4 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 yds4 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.6 yds4 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.6 yds4 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.6 yds4 yds 8 yds6 yds

7) Write an expression that shows how to find the area of the rectangle and uses the distributive property.6 yds4 yds 8 yds6 yds6 x 4

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

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