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I can use the distributive property to simplify expressions.

I can use the distributive property to simplify expressions. I can successfully solve 4 out of 5 classwork problems. Warm Up 1. Which is easiest to do mentally for you? A. 2 • 50 + 2 • 9 OR a. 2 • 59

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I can use the distributive property to simplify expressions.

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  1. I can use the distributive property to simplify expressions. I can successfully solve 4 out of 5 classwork problems. Warm Up 1. Which is easiest to do mentally for you? A. 2 • 50 + 2 • 9 OR a. 2 • 59 B. 3 • 436 OR b. 3 • 400 + 3 • 30 + 3 • 6 1 8 C. x 9_ OR c. 9 x 10 + 9 x 8 2. Simplify each expression above using order of operations. Are the two expressions equivalent in each? What is the solution?

  2. A. 2 • 50 + 2 • 9 OR 2 • 59B. 3 • 436 OR 3 • 400 + 3 • 30 + 3 • 6 1 8C. x 9_ OR 9 x 10 + 9 x 8 Think-Pair-Share 1. Were the solutions equivalent in the pairs of expressions? Why or why not… • What do you notice about the pairs of expressions? Similarities? Diffs?

  3. Which diagram below illustrates the expression 3(2+4)? Which illustrates 3 2 + 3 4 ? 2 4 2 + 4 3 3 Diagram A Diagram B Draw a similar diagram to show 4(3 + 5) and 4 * 3 + 4 * 5.

  4. Distributive Property The Distributive Property allows us to simplify things out of order from the order of operations by distributing things inside parenthesis. For Example: 3(x+2) We can’t simplify what’s in the parenthesis because we don’t know the value of x

  5. Distributive property But with the distributive property For example: 3(x+2) You simply multiply the number in front of the parenthesis with each part inside the parenthesis. = 3x + 3(2) = 3x+6 3(x+2)

  6. The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac and (b + c) a = ba + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5 • x + 5 • 7 5x + 35

  7. A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x2

  8. 3) The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y2 1

  9. Let’s practice: Evaluate the expressions. Back to notes! Example #2 3(m - 4) 3 • m - 3 • 4 3m - 12 Example #3 2(y + 3) 2 • y + 2 • 3 2y + 6 2y + 6

  10. Answer Now Which statement demonstrates the distributive property incorrectly?Hold up your finger(s) to indicate your answer. • 3(x + y + z) = 3x + 3y + 3z • (a + b) c = ac + bc • 5(2 + 3x) = 10 + 3x • 6(3k - 4) = 18k - 24

  11. Did we meet our Target? I can use the distributive property to simplify expressions. I can successfully solve 4 out of 5 classwork problems.

  12. Exit Ticket Explanation:There may be 1 problem in classwork that is for the exit ticket. 1. I have no idea how to do this 2. I can do it- do it 3. I can explain the steps 4. I can make a real world connection

  13. Classwork Use the Distributive Property to write 2 expressions that are represented by the area model. • (4 + 3) 2. 8 Evaluate the expressions. • 5(3+8) 4. 10(5.9+1.2) Rewrite the expression 5. n(15 + 25) 6. this is the exit ticket: c(4+6) 5 (3 + 1)

  14. I can use the distributive property to simplify expressions. I can successfully solve 4 out of 5 classwork problems. Warm Up

  15. Vocab Like Termsare terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

  16. WRITE: Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x3y, xy3 No, the exponents are on different variables.

  17. Answer Now Which of the following is the simplified form of 7x-4x ? (think “like terms”)Hold up your finger(s) to indicate your answer. • 3 • 3x • x • 11x

  18. are like terms and 5a and a are like terms The above expression simplifies to:

  19. WRITE: Simplify the expression1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2

  20. 7) y 5) 13a + 8a + 6b 21a + 6b 6) 4d + 6a2 - d + 12a2 18a2 + 3d

  21. Answer Now Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? • -36 • 3a - 36 • 8a - 36 • 8a + 36

  22. Did we meet our Target? I can use the distributive property to simplify expressions. I can successfully solve 4 out of 5 classwork problems.

  23. ClassworkSimplify the expression using the Distributive Property.

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