Distributive Property: Advanced Problems

1. Distributive Property:Advanced Problems It may be necessary to review the basic distributive property problems in the number property introduction PowerPoint presentation

2. 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

3. 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

4. Use the Distributive Property to write as an equivalent expression. Then evaluate the expression. Multiply. Add. Example 1-1a Answer: 52

5. 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

6. Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. a. b. Answer: Answer: Example 1-1c

7. 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.

8. 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.

9. 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).

10. 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

11. Use the Distributive Property to write as an equivalent algebraic expression. Simplify. Answer: Example 1-3a

12. Use the Distributive Property to write as an equivalent algebraic expression. Simplify. Answer: Example 1-3b

13. Use the Distributive Property to write each expression as an equivalent algebraic expression. a. b. Answer: Answer: Example 1-3c

14. Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as Distributive Property Simplify. Definition of subtraction Answer: Example 1-4a

15. Use the Distributive Property to write as an equivalent algebraic expression. Rewrite as Distributive Property Simplify. Answer: Example 1-4b

16. Use the Distributive Property to write each expression as an equivalent algebraic expression. a. b. Answer: Answer: Example 1-4c

17. Real-Life Example 2Mental Math

18. The distributive property is mental math strategy that can be used when multiplying. 43 x 5 =?

19. Break apart the double-digit number. 43 x 5 =? 40 3 +

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

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

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

23. Let’s look at another example. 53 x 6 = ?

24. Break apart the double-digit number. 53 x 6 = ?

25. Break apart the double-digit number. 53 x 6 = ? 50 3 +

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

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

28. Sum the two products. 53 x 6 = 318 50 3 + x 6x 6 300 + 18 = 318

29. The word “distribute” means “to give out.”

30. Distribute the cubes to the girls.

31. Distribute the cubes to the girls.

32. Distribute the cubes to the girls.

33. Distribute the cubes to the girls.

34. Distribute the cubes to the girls.

35. Distribute the cubes to the girls.

36. In this example, the 5 was distributed. 5 x 38 = 5 x (30 + 8) = (5 x 30) + (5 x 8)

37. In this example, the 7 was distributed. 7 x 46 = 7 x (40 + 6) = (7 x 40) + (7 x 6)

38. Find the area of the rectangle.Area = length x width 6 ft 24 ft

39. Find the area of the rectangle.Area = length x width 6 ft 24 ft

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

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

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

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

44. 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

45. 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

46. 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

47. 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

48. 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

49. 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

50. 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