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 × cand pictorially (rectangular array area model):

a × b a × ca

b c

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

symbolically:

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

6 × 10 6 × 36

10 3

Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.

Answer: 52

Multiply.

Add.

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.

Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression.

a.

b.

Answer:

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 Find the cost of 4 trips and 4 wet suits. Then add.

cost of 4 wet suitscost of 4 trips

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.

b. Find the total cost.

Answer: $45

Answer:

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.

b.Answer:

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.

Distributive Property

Simplify.

Answer:

Rewrite as

Use the Distributive Property to write each expression as an equivalent algebraic expression.

a.

b.Answer:

Answer:

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 products

43 x 5 =215

40 3 x 5 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 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 = 318

50 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 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 waterdeepwater8

yds

5 yds 10 yds

shallow waterdeepwater8

yds

5 yds 10 yds

8 yds

Break the pool into a deep end and a shallow end.

shallow waterdeepwater8

yds

5 yds 10 yds

8 yds

Find the area of the deep end.

shallow water8 x 5 = 40

8 yds

5 yds 10 yds

8 yds

Find the area of the deep end.

shallow water8 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.

80 408 yds

5 yds 10 yds

Now sum the two areas together.

+

80 408 yds

5 yds 10 yds

40 + 80 = 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:

2 + 3 + 2 + 3 and shows the distributive property.

2 x (2 + 3)

2 + 2 + 3 + 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) ?

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 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 yds

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 yds

4 x 3 4 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 yds

4 x 3 4 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

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

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 4 6 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 4 6 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

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

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 2 5 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 3 8 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

5x 5 ∙ 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 + 10

3x + 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 + 20 Correct!

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

8x + 16

8x + 2

10x

8x + 10

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

8x + 16 Correct!

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!

Click below to see video

• http://www.youtube.com/watch?v=nVbRzhOIgm0

• http://glencoe.mcgraw-hill.com/sites/007888523x/student_view0/chapter4/lesson1/personal_tutor.html

• http://www.youtube.com/watch?v=itmz8i62Ag4

Click to Test Your Skills• http://glencoe.mcgraw-hill.com/sites/007888523x/student

_view0/chapter4/lesson1/self-check_quizzes.html• http://www.algebrahelp.com/worksheets/view/simplifying/

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