Remember to read the textbook before attempting to do your homework. Answer: 1. Why? x is the same as 1 x, and 1 x = 1x


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1 Remember to read the textbook before attempting to do your homework. Section.6/.7: Simplifying Expressions Definitions: A variable is a letter used to represent an unknown number, e.g. x, y, z, m, n A number by itself is called a constant, e.g. 5,, 0,, 0.3, 3 5 7,.9, 9 4 A term is a constant or a variable, or a product of constants and variables, e.g., x, x 3, xy, 3 x An algebraic expression is a collection of numbers, variables, grouping symbols and operation symbols such as +,,,. e.g. 3x 6, 3 + [5(m ) + 6], 5xy 3z + 9 To evaluate an expression is to give the expression a numerical value by substituting a value for a variable and simplifying. The numerical coefficient (or coefficient) is the number in front of the variable, e.g. Looking at 7bc, 7 is called the coefficient, and bc is called the variable part. What is the coefficient of the term x 3? Answer: What is the coefficient of the term x? Answer: Why? x is the same as x, and x = x Moral of the story: If there is not a number written next to a variable, then the coefficient is understood to be. What is the coefficient of the term x 3? Answer: What is the coefficient of the term x? Answer: Why? x is the same as x, and x = x Moral of the story: If there is only a negative sign,, next to a variable, then the coefficient is understood to be. Example : Evaluate the expression for the given value of the variable. No calculators allowed. p 3pq + 5; p = 4, q = Please note: The answer is not 45. Example : Panchito needs your help. He has been assigned a set of homework problems. Write down every single problem that he will have to do for that assignment. Note: eoo means every other odd a. 7 odd, 6 0 ALL, 9 53 eoo b eoo No, Ms. Torres has not made a typeo CH LECTURE Notes by M. Torres Pg Math 60 Beginning Algebra
2 Definition: Like terms are terms that are constants, or terms that contain the same variable(s) raised to the same powers. e.g., 5, ¾, 0.5 all constants (numbers) x, 5x, 0.5x all have same variable part x, 4x all have same variable part 6x 3 y z 5, 7x 3 y z 5 all have same variable part FYI: The cool thing about like terms is that we can combine them. Combining Like Terms: To combine like terms, add or subtract their coefficients and keep the same variables with the same exponents. Example 3: Simplify. No calculators allowed. a. 6m m + 5m 8m + 37 b. 3 x 9x 6x + 9x c. (3a + 5a 4) c (3a + 5a 4) can be seen as... means what is the opposite of 3a + 5a 4? (3a + 5a 4) 3a 5a d. 5 x 4 x 7 6 e. n 4n 3 Ans: 4x + 45 Ans: 7 3 n 5 30 (end of Section.6/.7 combo unit, so.6 and.7 are assigned for homework today yay!) CH LECTURE Notes by M. Torres Pg Math 60 Beginning Algebra
3 (Sections.6 and.7, continued ) Are you looking for more math action? Then work on the next page: Math Pizzazz E6 Prealgebra Review (just in case you wanted to brush up on your prealgebra skills) Sets of Numbers: The set of NATURAL NUMBERS (aka counting numbers) is given by {,, 3, 4, 5, 6, 7, 8, 9, 0,,, 3, 4,, 99, 00, 0, 0, 03,, 099, 00, 0, } The set of WHOLE NUMBERS include the set of natural numbers and 0. {0,,, 3, 4, 5, 6, 7, 8, 9, 0,,, 3,, 99, 00, 0, 0, 03,, 099, 00, 0, } The set of INTEGERS includes the set of whole numbers and their opposites. { 0, 0, 00, 99,, 7, 6, 5, 4, 3,,, 0,,, 3, 4, 5, 6, 7,, 99, 00, 0, 0} Properties of real Numbers If a, b, and c are real numbers, then we have: Commutative Property of Addition: Commutative Property of Multiplication: a + b = b + a e.g. 3 + = + 3 (The order in which we add does not matter) Associative Property of Addition: a + (b + c) = (a + b) + c e.g. + (3 + 4) = ( + 3) + 4 a b = b a e.g. 3 = 3 (The order in which we multiply does not matter) Associative Property of Multiplication: a (b c) = (a b) c e.g. (3 4) = ( 3) 4 The way in which the numbers are grouped does not change their sum Additive Identity: (aka Identity Property of Addition) a + 0 = a, where 0 is the additive identity e.g = = 3 Additive Inverse: (aka Inverse Property of Addition) a + ( a) = 0, where a is the additive inverse e.g. 3 + ( 3) = = 0 Distributive Property (over addition): Note: additive inverse is code for opposite a(b + c) = ab + ac e.g. (x + 3) = x + 3 = x + 6 The way in which the numbers are grouped does not change their product Multiplicative Identity: (aka Identity Property of Multiplication) a = a, where is the multiplicative identity e.g. 3 = 3 3 = 3 Multiplicative Inverse: (aka Inverse Property of Multiplication) a a =, where a e.g. 3 3 = 4  = 4 Distributive Property (over subtraction): is the multiplicative inverse Note: multiplicative inverse is code for reciprocal a(b c) = ab ac e.g. (x 3) = x 3 = x 6 CH LECTURE Notes by M. Torres Pg 3 Math 60 Beginning Algebra
4 Remember to read the textbook before attempting to do your homework. Bonus Material for Chapter : Translating Verbal Expressions into Variable Expressions (Textbook reference: Section.) Tip: Key terms that you need to feel very comfortable with. Words that are code for... Addition Subtraction Multiplication Division add sum plus more than increased by subtract (from) difference minus less than decreased by less multiply product times twice twice: code for times of divide quotient with fractions and percent The word and is your friend! Why? Because that word separates the terms that you are adding, subtracting, multiplying, or dividing. Warning: Since subtraction is not commutative, you need to be very careful when writing expressions involving subtraction. Whenever you see the word difference, you need to subtract the terms in the order in which they are given. Warning: Since division is not commutative, you need to be very careful when writing expressions involving division. Whenever you see the word quotient, you need to divide the terms in the order in which they are given. Example : Write the algebraic expression described. Let x represent the unknown number. a. Fiveninths of the number e. Eighteen less than a number b. The quotient of eight and a number f. Four less than five times a number c. The sum of twice a number and seven. g. Twentysix more than ten times a number d. The difference of twelve and fourteen h. The difference of one and twice a number CH LECTURE Notes by M. Torres Pg 4 Math 60 Beginning Algebra
5 Example : Write the algebraic expression described. Let x represent the unknown number. a. Twice the difference of six and a number b. Three times the sum of a number and five c. Six less than twice the difference between a number and seven. d. Eight more than four times the difference of three times a number and negative five. e. The sum of oneeighth of a number and onetwelfth of the number. (You ve reached the official end of Chapter how exciting!!!) Don t forget to start working on today s homework in a timely manner that way you ll be on track to getting the grade that you are willing to earn. You can check out the textbook for FREE through the Library s Reserve System. Instructor also has extra copies of the textbook for you to use during her office times. Wait! Are you looking for more fun? Then work on the attached sheet: PreAlg. 4 CH LECTURE Notes by M. Torres Pg 5 Math 60 Beginning Algebra
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