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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
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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
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. Then evaluate the expression. Multiply. Add. Example 1-1a 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. Example 1-1b Answer: 30
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. a. b. Answer: Answer: Example 1-1c
cost for 1 person 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 of 4 trips cost of 4 wet suits Example 1-2a Method 2 Find the cost of 4 trips and 4 wet suits. Then add.
Distributive Property Multiply. Add. Example 1-2b Evaluate either expression to find the total cost. Answer: The total cost is$336. Check You can check your results by evaluating4($84).
Answer: 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
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. a. b. Answer: Answer: Example 1-3c
Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as Distributive Property Simplify. Definition of subtraction Answer: Example 1-4a
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. a. b. Answer: Answer: Example 1-4c
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 5x 5
Then multiply each part by 5. 43 x 5 =? 40 3 + x 5x 5 200 15
Finally, sum your two products 43 x 5 =215 40 3 + x 5x 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 6x 6
Multiply each part by 6. 53 x 6 = ? 50 3 + x 6x 6 300 18
Sum the two products. 53 x 6 = 318 50 3 + x 6x 6 300 + 18 = 318
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 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