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**1.2 Modeling Algebraic Expressions using tiles**

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**Which algebraic expression can be found of the next figure?**

What does the a represent? and b? and c? What kind of polygon has the area : A = ab + ac? c b Using the formula A= base X height, the area of any rectangle can be calculate base = a, height = b + c Area = a X ( b + c ) The expression (b+ c) indicates that this addition must be solved first and the sum should be multiplied by a. In this case, the multiplication sign can be omitted and writen as: A = a(b+c) a

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**1. How can the area of one of the rectangles be represented? **

2. If you add the areas made by the next three rectangles, how can you write the expression that represents the total area? x

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**Use the rectangle below to explain the next equality: 5(x + 4) = 5x + 20**

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**Now, try to explain the next equality: 11(x – 7) = 11x - 77**

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**Draw the rectangles that represent the next equalities**

9( x + 6) = 9x + 54 8(x – 4 ) = 8x - 32

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**As you noticed, parenthesis are used to indicate which operation must be solved first.**

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Exercises: Sebastian: Raise a number to the second power and then subtract 2, divide the difference by 5. Hortensia: Raise a number to the second power,divide it by 5, and then subract 2. Margarita: Raise a number to the second power and then subtract the quotient of 2 over 5 Can you tell which is Sebastian’s card, Hortensia’s card and Margarita’s card?

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**Write as an algebraic expression**

Eight times the difference of x and y Nine times the difference of y and z, increased by 3z Three times the sum of a and b, decreased by 7a

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**Match the algebraic expression with its equality**

4((x – 2) -8) a) 4x-10 4(x-2) -8 b) 4x-16 (4x-2-8) c) 4x-40

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