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## Distributive Property: Advanced Problems

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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