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): b c a a × b a × c
using your mental math skills . . . An example: 6 x 13 using your mental math skills . . . symbolically: 6 × (10 + 3) = 6 × 10 + 6 × 3 and pictorially (rectangular array area model): 10 3 6 6 × 10 6 × 3
Use the Distributive Property to write as an equivalent expression Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Multiply. Add. Answer: 52 Example 1-1a
Use the Distributive Property to write as an equivalent expression 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 Example 1-1b
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. a. b. Answer: Answer: Example 1-1c
Method 1 Find the cost for 1 person, then multiply by 4. 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 2 Find the cost of 4 trips and 4 wet suits. Then add. cost of 4 wet suits cost of 4 trips Example 1-2a
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). Example 1-2b
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: Answer: $45 Example 1-2c
Use the Distributive Property to write as an equivalent algebraic expression. Simplify. 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 each expression as an equivalent algebraic expression. Answer: Answer: Example 1-3c
Distributive Property Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as Distributive Property Simplify. Definition of subtraction Answer: Example 1-4a
Distributive Property Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as Distributive Property Simplify. Answer: Example 1-4b
Use the Distributive Property to write each expression as an equivalent algebraic expression. Answer: Answer: Example 1-4c
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 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.
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
Find the area of the rectangle. Area = length x width
Find the area of the rectangle. Area = length x width 20 ft + 4 ft
Find the area of the rectangle. Area = length x width 20 ft + 4 ft
Find the area of the rectangle. Area = length x width 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 24 sq ft 20 ft + 4 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 24 sq ft 20 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 20 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 20 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 and a deep end A swimming pool has a shallow end and a deep end. Find the surface area of the pool. deepwater 8 yds shallow water 5 yds 10 yds
Break the pool into a deep end and a shallow end. deepwater 8 yds 8 yds shallow water 10 yds 5 yds
Find the area of the deep end. deepwater 8 yds 8 yds shallow water 10 yds 5 yds
Find the area of the deep end. 8 x 5 = 40 8 yds 8 yds shallow water 10 yds 5 yds
Find the area of the shallow end. 8 x 5 = 40 8 yds 8 yds shallow water 10 yds 5 yds
Find the area of the shallow end. 8 x 5 = 40 8 yds 8 yds 8 x 10 = 80 10 yds 5 yds
Now sum the two areas together. 8 x 5 = 40 8 yds 8 yds 8 x 10 = 80 10 yds 5 yds
Now sum the two areas together. 40 80 + 8 yds 10 yds 5 yds
40 + 80 = 120 square yards 40 80 8 yds 5 yds 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) (9 x 20) 5 yds 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 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) ?
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) ?
5) Which of the following expressions is equivalent to: (5 x 9) + (5 x 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 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 yds 4 x 3 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 yds 4 x 3 4 x 9 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 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
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 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 6 yds 6 x 4 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 6 x 4 6 x 8 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 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
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 5 x 10 2 yds 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 8 x 5 3 yds 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 5x 5 ∙ 10 x yds 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)?
11) Which expression is equivalent to 3(x + 7)? Correct! 3x + 21
12) Which expression is equivalent to 4(x + 5)?
12) Which expression is equivalent to 4(x + 5)? Correct!
13) Which expression is equivalent to 8(x + 2)?
13) Which expression is equivalent to 8(x + 2)? Correct!
14) Which expression is equivalent to 2(x + 3)?
14) Which expression is equivalent to 2(x + 3)? 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/distribution.quiz http://algebralab.org/studyaids/studyaid.aspx?file=Algebra1_2-6.xml http://www.algebra-class.com/distributive-property-practice.html http://www.algebralab.com/practice/practice.aspx?file=Algebra1_2-6.xml