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 b c ab

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

10 3 6 10 63 Use the Distributive Property to write as an equivalent expression. Then evaluate

the expression. Multiply. Add. Answer: 52 Use the Distributive Property to write as an equivalent expression. Then evaluate

the expression. ***It doesnt matter which side of the parenthesis the number is on. The property works the same. Multiply. Add. Answer: 30 Use the Distributive Property to write each expression as an equivalent

expression. Then evaluate the expression. a. Answer: b. Answer: Real 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. cost for 1 person Method 2 cost of 4 trips

Find the cost of 4 trips and 4 wet suits. Then add. cost of 4 wet suits Evaluate either expression to find the total cost. Distributive Property Multiply.

Add. Answer: The total cost is $336. Check You can check your results by evaluating 4($84).

Movies 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. Answer: b. Find the total cost.

Answer: $45 Use the Distributive Property to write as an equivalent algebraic expression. Simplify. Answer:

Use the Distributive Property to write as an equivalent algebraic expression. Simplify. Answer: Use the Distributive Property to write each expression as an equivalent algebraic expression. a. Answer:

b. Answer: Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as Distributive Property

Simplify. Definition of subtraction Answer: Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as

Distributive Property Simplify. Answer: Use the Distributive Property to write each expression as an equivalent algebraic expression. a. Answer: b.

Answer: Real-Life Example 2 Mental 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 x5 + 3 x5 Then multiply each part by 5.

43 x 5 =? 40 x5 200 + 3 x5 15

Finally, sum your two products 43 x 5 =215 40 + 3 x5 x5

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 x6 + 3 x6 Multiply each part by 6. 53 x 6 = ? 50

x6 300 + 3 x6 18 Sum the two products. 53 x 6 =

318 50 + 3 x6 x6 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 width 6 ft 24 ft 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 6 ft

20 ft + 4 ft Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft

6 ft 20 ft + 4 ft Find the area of the rectangle. Area = length x width

Find the area of each rectangle. 6 ft 6 ft 6 x 20 = 120 sq ft 20 ft +

4 ft Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft

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

Find the area of the rectangle. Area = length x width Find the area of each rectangle. 6 ft 6 ft 120 sq ft 20 ft

+ 4 ft 24 sq ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together.

6 ft 6 ft 120 sq ft 20 ft + 4 ft

24 sq ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq ft

20 ft 24 sq ft + 4 ft Find the area of the rectangle. Area = length x width Now put the two rectangles back together.

6 ft 120 sq ft 20 ft + 4 ft 24 sq ft

Find the area of the rectangle. Area = length x width Now put the two rectangles back together. 6 ft 120 sq + 24 sq ft ft 24 ft Find the area of the rectangle.

Area = length x width Now put the two rectangles back together. 6 ft 144 sq ft 24 ft A swimming pool has a shallow end and a deep end. Find the surface

area of the pool. 8 yds deepw ater 5 yds shallow water

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

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

8 yds deepw ater 5 yds 8 yds

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

5= 40 5 yds 8 yds shallow water 10 yds

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

8 yds shallow water 10 yds Find the area of the shallow end. 8

yds 8x 5= 40 5 yds 8 yds

8 x 10 = 80 10 yds Now sum the two areas together. 8 yds 8x

5= 40 5 yds 8 yds 8 x 10 = 80

10 yds Now sum the two areas together. 8 yds 40 5 yds

+ 80 10 yds 40 + 80 = 120 square yards 8 yds

40 5 yds 80 10 yds 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

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

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

9 yds (9 x 5) 5 yds + (9 x 20)

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

5 yds 20 yds Practice Time 1) Which of the following expressions shows the distributive property for 5 x (3 + 7)? (5 + 3) x (5 + 7)

(5 x 3) x (5 x 7) (5 x 3) + (5 x 7) 1) Which of the following expressions shows the distributive property for 5 x (3 + 7)? Correct! (5 x 3) + (5 x 7)

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+2+3+3 2 x (2 + 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) ? 3 x (4 + 8) 8 x (3 + 4) 4 x (3 + 8) 4) Which of the following expressions is equivalent to: (4 x 3) + (4 x 8) ? Correct! 4 x (3 + 8)

5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 3) ? 3 x (9 + 5) 5 x (9 + 3) 9 x (3 + 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 4 yd

s 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

4x3 3 yds 4 yd s 9 yds 6) Write an expression that shows how to

find the area of the rectangle and uses the distributive property. 4 yds 4x3 3 yds 4

yd s 4x9 9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4x3

4 yds 4x9 4 yd s 3 yds

9 yds 6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4x3 4x9 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. 4x3 4x9

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. 4x3 +

4x9 4 yds 3 yds 9 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 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds

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 6x4 4 yds 6 yds 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 yds 6x4 4 yds

6 yds 6x8 8 yds 7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6x4

6 yds 6x8 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. 6x4 6x8 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. 6x4 6x8 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. 6x4 + 6x8

6 yds 4 yds 8 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 8) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5

yds 5x2 2 yds 5 x 10 10 yds 8) Write an expression that shows how to

find the area of the rectangle and uses the distributive property. 5x2 + 5 x 10 5 yds 2 yds 10 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

9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8 yds 8x3 3 yds

8x5 5 yds 9) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 8x3 +

8x5 8 yds 3 yds 5 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 10) Write an expression that shows how to find the area of the rectangle and uses the distributive property.

5 yds 5x x yds 5 10 10 yds

10) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 5x + 5 10 5 yds x yds

10 yds 11) Which expression is equivalent to 3(x + 7)? x + 10 x + 21 3x + 7 3x + 21 11) Which expression is equivalent to 3(x + 7)?

3x + 21 Correct! 12) Which expression is equivalent to 4(x + 5)? x+9 4x + 20 4x + 5 9x

12) Which expression is equivalent to 4(x + 5)? 4x + 20 Correct! 13) Which expression is equivalent to 8(x + 2)? 10x

8x + 2 8x + 16 8x + 10 13) Which expression is equivalent to 8(x + 2)? 8x + 16 Correct!

14) Which expression is equivalent to 2(x + 3)? 2x + 6 2x + 5 2x + 3 2x + 2 14) Which expression is equivalent to 2(x + 3)? 2x + 6

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