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**Chapter 1 Lesson 1 Variables and Expressions**

Objective: Evaluate expressions containing variables and translate verbal phrases into algebraic expressions.

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**Operation Vocabulary – What Each Sign Means**

+ - x plus sum more than increased by total in all minus difference less than subtract decreased by times product multiplied each of divided quotient

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**Examples Translate each phrase into an algebraic expression.**

a number decreased by eight Let n represent the number. The words ‘decreased by’ suggests subtraction. The algebraic expression is n – 8. b. seven more than twice as many dollars. Let d represent dollars. The words ‘more than’ suggest addition and the word twice is another way of saying ‘two times’. The algebraic expression is 7 + 2d or 2d + 7

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**Examples Translate each phrase into an algebraic expression.**

c. a number increased by eight Let b represent the number. The words ‘increased by’ suggests addition. The algebraic expression is b + 8. d. 15 plus the quotient of 20 and x. The word ‘plus’ means addition. The words ‘quotient’ suggest divide. The algebraic expression is /x or 20/x + 15

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**Examples Translate each algebraic expression into a phrase. e. 7h**

Two things beside each other mean multiply. Answer: seven times h or seven multiplied by h f. 5 - x What you have to be careful about here is that you get your words in the right order. Are you subtracting 5 from x or x from 5? Whatever is second is being subtracted from the first. Answer: x subtracted from 5 3m + 2 Answer: two added to three times m OR two more than three times m OR three times m plus 2 There are several different ways to write this!

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A Little Harder… Draw a picture representing a rectangle whose length is eight less than four times its width. Write an expression for the perimeter of the rectangle. We know something about the length but have no clue about width, so…width is our variable. Eight less than means subtract. Four times means multiply. So subtract eight FROM four times. Now, how do you find perimeter? Add up all the sides! w + w + 4w – 8 + 4w – 8 Do you remember how to combine like terms? 10w - 16 w 4w - 8

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$100 $200 $300 $400 $100 $200 $300 $400 $300 $200 $100 Writing variable equations Find variables in addition equations Find variables in subtraction.

$100 $200 $300 $400 $100 $200 $300 $400 $300 $200 $100 Writing variable equations Find variables in addition equations Find variables in subtraction.

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