Equiavlent Algebraic Expressions.pptx

This is a presentation explaining how to simplify equivalent algebraic expressions

1. Equivalent Algebraic Expressions

2. We learned how to evaluate an algebraic expression using a skill called substitution .

3. Step 1: Substitute (or replace) the variable with the given number. Step 2: Solve the expression Example Evaluate 2y + 3 when y = 4 2( 4 ) +3 8 + 3 11 To evaluate an algebraic expression when you are given the value of a variable:

4. We are going to use these skills to determine if two algebraic expressions are equivalent expressions . We will start with an exploration to see if you can discover on your own what makes two expressions equivalent.

5. Exploration ( Set – A ) Evaluate each expression for the given values. For each value that you plugged in… Did the answer for Expression A and Expression B calculate to be the same? Yes or No

6. Exploration ( Set – B ) Evaluate each expression for the given values. For each value that you plugged in… Did the answer for Expression A and Expression B calculate to be the same? Yes or No

7. Exploration ( Set – C ) Evaluate each expression for the given values. For each value that you plugged in… Did the answer for Expression A and Expression B calculate to be the same? Yes or No

8. Finding Equivalent Expressions

9. How do I know if Two Expressions are Equivalent? Method 1: Substitute Values Substitute several values into each expression as we did in the Explore Activity . If they calculate to be the same number in every situation then they are equivalent expressions. Method 2: Simplify & Match You can apply the properties of operations to simplify each expression. If the simplified versions of both expressions are identical, then you can say that they are equivalent expressions.

10. Let’s take a look at a problem where the Simplify & Match Method would be a good method to use to determine if expressions are equivalent…

11. EXAMPLE - Simplify & Match Method Which expression is equivalent to 7(x + 4) ? A. x + 11 B. x + 28 C. 7x + 4 D. 7x + 28 First Ask Yourself… Is there anything that we need to simplify in the question or answer choices to generate identical expressions? If yes, then… Apply the appropriate property and match.

12. You need to understand that BOTH methods will work for every single problem, but in some cases one method may be easier to use than the other. Let’s take some problems and use both methods to determine if the expressions are equivalent.

13. Guided Practice #1 Are the expressions 3x + 5 and 3(x+5) equivalent expressions? Use both methods to justify your answer. Method 1 Substitute Values Method 2 Simplify & Match

14. Guided Practice #2 Are the expressions 2y + 5 and 5 + 2y equivalent expressions? Use both methods to justify your answer. Method 1 Substitute Values Method 2 Simplify & Match

15. Guided Practice #3 Are the expressions 3x and (x)(x)(x) equivalent expressions? Use both methods to justify your answer. Substitute Values Method Simplify & Match Method

16. Select ALL of the expressions that are equivalent to 10 (x + 6). First… simplify the expression in the question by distributing 10x +60 60 + 10x 10x + 60 10x + 6 10x + 50 + 10 5(2x + 12) 2(5x + 6) Already Simplified - Match (Commutative Property of Addition) Already Simplified - Match Already Simplified - Does NOT Match Must Simplify to 10x + 60 - Match Must Simplify to 10x + 60 (Distributive Property) - Match Must Simplify to 10x + 12 (Distributive Property) - Does NOT Match

17. Now you can try these next 5 problems…

18. You Try #1 Which expression is equivalent to 2(6x+3)? A. 12x + 3 B. 6x + 6 C. 3(4x + 2) D. 12(x + 3) Use Simplify & Match… Is there anything that we need to simplify in the question or answer choices to generate identical expressions?

19. You Try #2 Which expressions are equivalent to 9w + 6? SELECT ALL that apply. 6 + 9w 9w + 4 + 5 9(w + 6) 3(3w + 2) 3(3w + 6) Use Simplify & Match Method… Is there anything that we need to simplify in the question or answer choices to generate identical expressions?

20. You Try #3 Use Simplify & Match Method… Is there anything that we need to simplify in the question or answer choices to generate identical expressions? Select ALL the expressions that are equivalent to 4(3 + 5x). 12 + 5x 20x + 12 12 + 20x 6 + 6 + 5x 2(6x + 10) 4(5x + 3)

21. You Try #4 Determine if the expressions below are equivalent by substituting in values for x . Use the following values: 1, 2, x² + 2 2x + 1 + 1 Do any other values work?

22. You Try #5 Determine if the expressions below are equivalent expressions by substituting 2 values of your choice for m . 14m + 16m 30m 2m(7 + 8)

23. Thank You