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The Distributive Property

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Presentation on theme: "The Distributive Property"— Presentation transcript:

1 The Distributive Property
Apply the associative, commutative, and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers

2 I can… Self Assessment Use the distributive property of multiplication
5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

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

4 Distribute the cubes to the girls.

5 Distribute the cubes to the girls.

6 Distribute the cubes to the girls.

7 Distribute the cubes to the girls.

8 Distribute the cubes to the girls.

9 Distribute the cubes to the girls.

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

11 Break apart the double-digit number.
43 x 5 =? +

12 Then multiply each part by 5.
43 x 5 =? + x 5 x 5

13 Then multiply each part by 5.
43 x 5 =? + x 5 x 5

14 Let’s look at another example.

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

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

17 Multiply each part by 6. 53 x 6 = ? + x x 6

18 Multiply each part by 6. 53 x 6 = ? + x x 6

19 Add the two products. 53 x 6 = 318 + x x 6 = 318

20 3 steps to the distributive property.
4 x 28 =

21 3 steps to the distributive property.
4 x 28 = 1) Break apart the double-digit number.

22 3 steps to the distributive property.
4 x 28 = 4 x (20 + 8) 1) Break apart the double-digit number.

23 3 steps to the distributive property.
4 x 28 = 4(20 + 8) Break apart the double-digit number. Multiply each part by 4. (distribute the 4)

24 3 steps to the distributive property.
4 x 28 = 4 (20 + 8) = (4 x 20) + (4 x 8) Break apart the double-digit number. Multiply each part by 4. (distribute the 4)

25 3 steps to the distributive property.
4 x 28 = 4 (20 + 8) = (4 x 20) + (4 x 8) Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Sum the two products.

26 3 steps to the distributive property.
4 x 28 = 4 (20 + 8) = (4 x 8) Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Sum the two products.

27 3 steps to the distributive property.
4 x 28 = 4 (20 + 8) = Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Add the two products.

28 3 steps to the distributive property.
4 x 28 = 4 (20 + 8) = = 112 Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Add the two products.

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

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

31 (5 + 3) x (5 + 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(3 + 7)? (5 + 3) x (5 + 7) (5 x 3) x (5 x 7) (5 x 3) + (5 x 7)

32 1) Which of the following expressions shows the distributive property for 5(3 + 7)?
Correct! (5 x 3) + (5 x 7)

33 (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(9 + 4) ? (3 x 9) + (3 x 4) (3 + 9) + (3 + 4) (3 + 9) x (3 + 4)

34 2) Which of the following expressions shows the distributive property for 3(9 + 4) ?
(3 x 9) + (3 x 4) Correct!

35 3) Which of the following expressions is equivalent to: and shows the distributive property. 2 (2 + 3) 3 (2 + 3)

36 3) Which of the following expressions is equivalent to: and uses the distributive property. 2 (2 + 3) Correct!

37 4) Which expression is equivalent to 3(x + 7)?

38 4) Which expression is equivalent to 3(x + 7)?
Correct! 3x + 21

39 5) Which expression is equivalent to 4(x + 5)?

40 5) Which expression is equivalent to 4(x + 5)?
Correct!

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

42 6) Which expression is equivalent to 8(x + 2)?
Correct!

43 7) Which expression is equivalent to 2(x + 3)?

44 7) Which expression is equivalent to 2(x + 3)?
Correct!

45 t = 5(40) + 30 t = 40 + 30 t = 5(40)- 5(30) t = 5(40+30)
8) Your class held a two-day car was. The class washed 40 cars on the first day and 30 cars on the second day. The class charged $5 for each car. Which equation can be used to find t, the total amount of money? t = 5(40) + 30 t = t = 5(40)- 5(30) t = 5(40+30)

46 8) Your class held a two-day car was
8) Your class held a two-day car was. The class washed 40 cars on the first day and 30 cars on the second day. The class charged $5 for each car. Which equation can be used to find t, the total amount of money? t = 5(40+30)

47 100 + 12 112 9) Use the Distributive Property to solve…
2(50 + 6) = _____ 112

48 86 - 24 62 10) Use the Distributive Property to solve…
10(8.6 – 2.4) = _____ 62

49 Daily Check 3.3 in your math notebook 7(50+9) 10(3.7-1..8) 9(96)
Find the product using the distributive method. Show your work!!!! 7(50+9) 10( ) 9(96) (3.8)6 A car travels an average of 24.7 miles per gallon of gas. How far can it travel on 8 gallons of gas?


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