Today we use the distributive property in equations and expressions with variables.

1. Today we use the distributive property in equations and expressions with variables. distributive=to give out

2. When you see a number next to another number in parentheses, this means to multiply. For example: 8(8)= 64 What are other ways to arrange problems that lets you know that you have to multiply? 8(8 x y)

3. Term • When you have numbers in parentheses, you call these numbers in parentheses, terms. • For example: • (9 + 6) is a term • (6 – y ) in a term

4. Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number An example is: 5(3 + t) = 5 × 3 + 5 × t product=multiplication

5. Distributive Property 5(3 t) = + 5(3 + t) = 5 × 3 5 × t In summary, when you multiply the 5 and the 3 And the 5 and the t you get 5 x 3 + 5 x t

6. Distributive Property 8(k 2) = - 8(k - 2) = 8 × k 8× 2 In summary, when you multiply the 8 and the k And the 8 and the 2 you get 8 x k - 8 x 2

7. Distributive Property 5(3 + t) = 5 × 3 + 5 × t Notice how the 5 is distributed by first multiplying with the 3 and then the 1.

8. Distributive Property 5(3 + t) = 5(3 + t) = 5 × 3 When you multiply the 5 and the 3 you get 5 x 3

9. Distributive Property 5(3 + t) = 5(3 + t) = 5 × 3 + 5 × t When you multiply the 5 and the 1 you get 5 x t

10. Let’s look at Distributive Property in a different way states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number An example is: (5 x 6) + (5 x t)=5(6 + t)

11. Why does this happen (5 x 6) + (5 x t)= + What is the common factor in the above equation? You factor it out What remains in the 1st term? What remains in the 2nd term? What operation is being done? 5( ) 6 t

12. Why does this happen (8 x r) - (8 x 6)= - What is the common factor in the above equation? You factor it out What remains in the 1st term? What remains in the 2nd term? Once the numbers and variables are in the parentheses, what do you do to the new term? 8( ) r 6

13. Why else is it important to use the distributive property in equations and expressions with variables • It is important to use the distributive property to be able to solve complex problems • It will also prepare you for algebra which you have to pass in order to graduate high school

14. We are going to use the distributive property in equations and expressions with variables • When they look like this: • (5 + 6) + ( 5 + y) • You look at both terms and find the common factor in both terms • 5 • You place the number that you factored, outside of the parentheses • 5( ) • You look at what remains in the first term and you place it in the parentheses • 5(6 ) • You look at what remains in the second term and you place it in the parentheses • 5(6 Y) • Look at the operation sign between both terms and place that in your new term • 5(6 + y) When they look like this: 6( 5 + y)= • You distribute (multiply) the factor (6) with the first number in the term and place them in a parentheses ( 6 x 5) • You distribute (multiply) the factor (6) with the second number in the term and place them in a parentheses ( 6 x y) • You place both terms together and include the operation sign found inside the original term (6 x 5) + (6 + y)

15. Let’s try one together • (8 + 6) + ( 8 + h) • You look at both terms and find the common factor in both terms • You place the number that you factored, outside of the parentheses • You look at what remains in the first term and you place it in the parentheses • You look at what remains in the second term and you place it in the parentheses • Look at the operation sign between both terms and place that in your new term 8 8( ) . 8(6 ) 8(6 h) 8(6 + h)

16. Let’s try one together • 7( 6 + g) • You distribute (multiply) the factor (7) with the first number in the term and place it in parentheses • You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses • You place both terms together and include the operation sign found inside the original (7 x 6) . (7 x g) (7 x 6) + (7 x g)

17. Let’s do two steps at a time • (8 + 6) + ( 8 + h) • You look at both terms and find the common factor in both terms • You place the number that you factored, outside of the parentheses • You look at what remains in the first term and you place it in the parentheses • You look at what remains in the second term and you place it in the parentheses • Look at the operation sign between both terms and place that in your new term 8 8( ) . 8(6 ) 8(6 h) 8(6 + h)

18. Let’s try two steps at a time • 7( 6 + g) • You distribute (multiply) the factor (7) with the first number in the term and place it in parentheses • You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses • You place both terms together and include the operation sign found inside the original (7 x 6) . (7 x g) (7 x 6) + (7 x g)

19. Let’s do them all on our own! • (8 + 6) + ( 8 + h) • You look at both terms and find the common factor in both terms • You place the number that you factored, outside of the parentheses • You look at what remains in the first term and you place it in the parentheses • You look at what remains in the second term and you place it in the parentheses • Look at the operation sign between both terms and place that in your new term 8 8( ) . 8(6 ) 8(6 h) 8(6 + h)

20. Let’s do all the steps together! • 7( 6 + g) • You distribute (multiply) the factor (7) with the first number in the term and place it in parentheses • You distribute (multiply) the factor (7) with the second number in the term and place them in a parentheses • You place both terms together and include the operation sign found inside the original (7 x 6) . (7 x g) (7 x 6) + (7 x g)

21. Let’s review what we learned: • What is distributive? • Why is a term? • What do you think is the most important reason to know how use the distributive property in equations and expressions with variables? Do one last problem! (3 + 5) – (3 + s)=