The Distributive Property 6.2.2.1 Apply the associative, commutative, and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers

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.

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.

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

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

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

3 steps to the distributive property. 4 x 28 =

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

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

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)

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)

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.

3 steps to the distributive property. 4 x 28 = 4 (20 + 8) = 80 + (4 x 8) Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Sum the two products.

3 steps to the distributive property. 4 x 28 = 4 (20 + 8) = 80 + 32 Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Add the two products.

3 steps to the distributive property. 4 x 28 = 4 (20 + 8) = 80 + 32 = 112 Break apart the double-digit number. Multiply each part by 4. (distribute the 4) Add the two products.

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

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

(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)

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

(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)

2) Which of the following expressions shows the distributive property for 3(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 (2 + 3) 3 (2 + 3)

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

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

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

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

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

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

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

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

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

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 = 40 + 30 t = 5(40)- 5(30) t = 5(40+30)

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)

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

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

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(3.7-1..8) 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?