MATH 010 KEVIN JONES BEGINNING ALGEBRA CHAPTER 1 REAL NUMBERS 1.1 Intro to Integers :inequalities > :opposites (-) :absolute values |x|

1.2 Add/Subtract Integers SAME SIGNS: Add their absolute values and keep the same sign. DIFFERENT SIGNS: Find the difference of their absolute values and keep the sign of the largest absolute value.

1.3 Multiply & Divide Integers Same Signs: Signs are the same the answer will be positive. Different Signs: Signs are different the answer will be negative.

Properties of Zero and One in Division > 0 divided by any number =0 >any number divided by the same number equals one. >any number divided by one equals the number

>any number divided by zero is not defined. a0a0 0  a

RATIONAL NUMBERS: A number that can be written Where a and b are integers and B cannot = 0 WHY?

Simplest Form: reduce so the numerator and the denominator have no common factor. Decimals: also rational numbers Repeating - Terminating - =

Addition of Fractions Find the LCM of 8 & 6 8=2*2*2 6=2*3 LCM= 2 *2 *3= = Reduce if possible

Exponents (powers) 333=3³ bbb=b³ b is the base 3 is the exponent

Evaluate (-2) =(-2)(-2)(-2)(-2) = 16 Evaluate –2 = = -16 (-a) even =positive (-a) odd =negative

ORDER OF OPERATIONS Please Excuse My Dear Aunt Sally P►parentheses, do what inside grouping symbols first ( ), { }, | |, [ ], and Fraction Bar

Excuse: simplify exponents My Dear: multiply or divide left to right. Aunt Sally: add or subtract left to right

Example: evaluate (8-5) ÷ 2² 12 – 24(3) ÷ 2² 12 – 24 (3) ÷ 4 12 – 72 ÷ 4 12 – 18 -6

Example (2) 6 ÷ [4 - (6 – 8)] + 2² 6 ÷ [4 – (-2)] + 2² 6 ÷ 6 + 2² 6 ÷ ►= 5

CHAPTER 2 VARIABLE EXPRESSION Variable expression is an expression that contains one or more variables 3x² - 5y + 2xy – x – 7 5 terms Variable terms: 3x², -5y, 2xy, -x Constant term: -7

Evaluating Variable Expressions Evaluate: x² - 3xy when x = 3 & y = -4 (3)² - 3(3)(-4) substitute 9 – 3(3)(-4)

Simplify Variable Expressions Variable Term; a term with a variable 3x² or 3xy or 3x²y³ Parts of a Term: 3x² 3 called the coefficient x called the variable 2 called the exponent The variable and the exponent are called the VARIABLE PARTS

LIKE TERMS: terms with the same variable parts. Combining like terms to simplify. 2x + 3x add the coefficients 5x Simplify: 7y – 10y +5 -5y + 5 Combine 7y and –10y, 5 is not a like term.

Steps to simplify variable expressions: 1. Remove all grouping symbols. 2. Look to collect the like terms.

Ex(1) Simplify 7(4 + 2x) Distribute the x No like terms Ex(2) Simplify 2n – 3(2n – 7r) Distribute the -3 2n – 6n + 21r Collect like terms -4n + 21r

Ex. 3 Simplify -7x + 3[x – (3 – 2x)]Parentheses -7x + 3[x – 3 +2x] Bracket -7x +3x – 9 + 6x Collect like terms 2x - 9

Translate Verbal Expressions into Variable Expressions Key words: Addition added to more than the sum of increased by the total of

Subtraction: minus *less than* decreased by the difference between Multiplication: times of the product of multiplied by

Division: divided by the quotient of the ratio of always use a fraction bar not ÷ Power (exponent): the square of the second power of the cube of the third power of the fifth power of

Ex: 1 Translation “The total of 3 times n and n” When a sentence starts with an operation, such as the total, then the and is where you would place that operation. “The total of 3 times n and n” 3n + n

Ex: 2 Translations “A number added to the product of four and the square of the number” Number → n Added → + Product of → and connects what will be multiplied. Four, square of the number→4n² n + 4n²

Ex: 3 Translation “a number multiplied by the total of six and the cube of the number” multiplied by the total > this is what I call back to back oper- ations and you must use a parentheses n(6 + n³) *first ( is for the multiplication.

Objective C Ex: 1 Translate “The height of a triangle is 10 ft longer than the base of the triangle. Express the height of the triangle in terms of the base of the triangle.” We are comparing the height to the length of the base, so let the length of the base be your variable. Base = x, so then the height = x + 10

Ex 2 Translate A rope 12 ft long was cut into two pieces of different length. Express The length of each piece. Smaller = Larger = X 12 - X This is called a sum of two unknowns