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# Ch1notes - Section 1-1Writing Expressions and Equations...

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Section 1-1—Writing Expressions and Equations Background: 1. An algebraic expression can contain numbers, variables, powers, and operations (addition, subtraction, multiplication, and division), but NO equal sign. For example: 3x + 4 5x 6xy x - y 2. A numerical expression contains numbers, powers, and operations. For example: 7 + 5 2 – 3 • 4 3 7 3. An algebraic equation is an algebraic expression that also contains an equal sign 4. Word and Symbols Equivalencies Addition Symbol plus “the sum of”, “and” increased by more than added to + the total of Subtraction Symbol minus decreased by “the difference of”, “and” fewer than - subtracted from Multiplication Symbol times “the product of”, “and” multiplied by at ( ) x of Division Symbol divided by “the quotient of”, “and” the ratio of fraction bar ÷ per Switch than from Equal Sign is equal to is the same as is as much as = is identical to

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Procedure and Examples: A. Writing an algebraic expression for each verbal expression-- 1. Replace each word with a symbol or number If the word sum, difference, product, or quotient is used then replace the word “and” with the correct symbol If the word “than” or “from” is used then switch the order of the numbers or variables directly before and after the operation (for example the number or variable before the operation goes after the operation, and the number or variable after the operation goes before the operation Parentheses can only be written using the words “sum, difference, product, and quotient” 2. Reduce the fraction 3. Rewrite the ratio as a to b or a: The numerator is the first number The denominator is the second number A. Examples: On a separate sheet of paper, write an algebraic expression for each verbal expression-– 1. Four more than t 2. eleven decreased by the quotient of x and 2 3. the product of 7 and x increased by 5 is nine 4. the quotient of p and 8 5. seven less than three times g is 3 6. twelve subtracted from the sum of g and 8 B. Writing a verbal expression for each algebraic expression-- 1. Replace each symbol or number with a word 2. If the word sum, difference, product, or quotient is used then replace the word “and” with the correct symbol If parentheses are needed then the words “sum, difference, product, and quotient” must be used B. Examples: On a separate sheet of paper, rite an algebraic expression for each verbal expression — 1. 7 q 2. 3x – 8 3. 10 = 4r – 6 4. 5(b – 3) 5. = 20 8 t 6. 7 = (8 + q) 2
Section 1-2—Order of Operations Background: 1. The order of operations is the order in which a problem with many steps in it is solved. 2. The saying “Please excuse my dear Aunt Sally” is used frequently to remember the order of operations.

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