Dr Fowler CCM Distributive Property Advanced Problems Distributive

Dr. Fowler CCM Distributive Property: Advanced Problems

Distributive Property a × (b + c) = a × b + a × 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 6× 3

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 doesn’t 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 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 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 x 5 + 3 x 5

Then multiply each part by 5. 43 x 5 =? 40 x 5 200 + 3 x 5 15

Finally, sum your two products 43 x 5 =215 40 + 3 x 5 200 + 15 = 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 = ? 50 + 3

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

Multiply each part by 6. 53 x 6 = ? 50 x 6 300 + 3 x 6 18

Sum the two products. 53 x 6 = 318 50 + 3 x 6 300 + 18 = 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 20 ft + 4 ft

Find the area of the rectangle. Area = length x width Find the area of each rectangle. 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 x 20 = 120 sq ft 20 ft 6 ft + 4 ft

Find the area of the rectangle. Area = length x width Find the area of each rectangle. 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 120 sq ft 20 ft 6 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 6 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 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 + 24 sq 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 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 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 8 x 5 = 40 5 yds 8 yds shallow water 10 yds

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

Find the area of the shallow end. 8 yds 8 x 5 = 40 5 yds 8 x 10 = 80 10 yds

Now sum the two areas together. 8 yds 8 x 5 = 40 5 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 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 4 x 3 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 4 x 3 3 yds 4 yd s 4 x 9 9 yds

6) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 4 x 3 4 yds 4 x 9 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 x 3 4 x 9 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 x 3 + 4 x 9 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 6 x 4 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 6 x 4 4 yds 6 x 8 8 yds

7) Write an expression that shows how to find the area of the rectangle and uses the distributive property. 6 x 4 6 yds 6 x 8 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 x 4 6 x 8 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 x 4 + 6 x 8 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 5 x 2 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. 5 x 2 + 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 8 x 3 3 yds 8 x 5 5 yds

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

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

11) Which expression is equivalent to 3(x + 7)? 3 x + 21 Correct!

12) Which expression is equivalent to 4(x + 5)? x+9 4 x + 20 4 x + 5 9 x

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

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

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

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

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

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