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Simplifying Algebraic Expressions with Distributive Property

Learn how to simplify algebraic expressions using the distributive property. Understand the concept and practice with numerical and algebraic equations.

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Simplifying Algebraic Expressions with Distributive Property

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  1. Thursday, April 24, 2014 Challenge Question: How do you simplify Algebraic expressions using Distributive Property? • Warm-Up: Complete the warm-up in your journalwith 0 noise level! • Solve the following problems: • 5(6 – 2) = • 11(12 + 4) = • (-19 + 11)8 = Directions: Please come in and get your journal. Title: Distributive Property

  2. Objective • Students will use the distributive property to re-write numerical and algebraic equations.

  3. The Distributive Property • The distributive property states: • To multiply a number by a sum, multiply each number inside the parentheses by the number outside the parentheses • The distributive property can be used with multiplication and addition or multiplication and subtraction • Let’s see what it looks like…

  4. Example 1 5(3 + 2) 15 + 10 = 25 Proof: 5(3+2) = 5(5) = 25

  5. Algebraic Expressions • The distributive property can be used to re-write algebraic expressions. • Use the same process…multiply what’s on the outside of the parenthesis by each term within the parenthesis • Let’s see what that looks like…

  6. Example 2 3(x + 1) 3x + 3 Note: In this instance 3x and 3 are not like terms. Therefore, you cannot combine them…so the expression is simplified to just 3x + 3

  7. Distributive Property • There are 2 ways that you can see the distributive property • With the multiplier on the left of the parenthesis • With the multiplier on the right of the parenthesis Example 5(2 + 3) OR (b + 3)5 In either event you multiply what’s on the out side of the parenthesis with EACH term inside the parenthesis

  8. Comments • The distributive property is a key algebraic concept…make no mistake about it…you are REQUIRED to be able to recognize and work with the distributive property if you are to pass Algebra 1, which is the first high school math class you will take!

  9. Common Errors • The most common error that students make when working the distributive property is that they only multiply what on the outside of the parenthesis with the first term within the parenthesis • The other common error is that students get the signs wrong…I do not give partial credit for incorrect signs!

  10. Your turn • In the notes section of your notebook use the distributive property to rewrite the expression • 8(x + 7) – 2x • (b + 9)6 -14 • 27 + (6 – z)5

  11. Learning Together • Complete the Distribute the Fun coloring page with a partner

  12. Just For Me • Complete the Multi-Step Equations coloring page on your own. • Use your notes to help you! • When finished, make sure your name is on it and turn it into the bin.

  13. Assessment • Ticket out the Door: 2(3x – x + 19) -12

  14. Wrap-Up • Put your journal back in your bin • HW: Multi-Step Equations coloring sheet (if not finished)… due Monday 4/28 at the beginning of class

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