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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 Presentation

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• 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 1-1c

• 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