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 ×

Example 1-1a Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Answer: 52 Multiply. Add.

Example 1-1b Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. ***It doesn’t matter which side of the parenthesis the number is on. The property works the same. Answer: 30 Multiply. Add.

Example 1-1c Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. a. b. Answer:

Example 1-2a 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

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

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

Example 1-2c 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. b.Find the total cost. Answer: $45 Answer:

Example 1-3a Use the Distributive Property to write as an equivalent algebraic expression. Simplify. Answer:

Example 1-3b 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. b. Example 1-3c Answer:

Example 1-4a Use the Distributive Property to write as an equivalent algebraic expression. Rewriteas Distributive Property Simplify. Definition of subtraction Answer:

Example 1-4b Use the Distributive Property to write as an equivalent algebraic expression. Distributive Property Simplify. Answer: Rewriteas

Use the Distributive Property to write each expression as an equivalent algebraic expression. a. b. Example 1-4c 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 =?

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

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

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

Let’s 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 = ?

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

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

Sum the two products. 53 x 6 = x 6 x = 318 +

The word “distribute” means “to give out.”

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 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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