1.1 Fractions Multiplying or dividing the numerator (top) and the denominator (bottom) of a fraction by the same number does not change the value of a fraction. Writing a fraction in lowest terms: Factor the top and bottom completely Divide the top and bottom by the greatest common factor

1.1 Fractions Multiplying fractions: Dividing fractions:

1.1 Fractions Adding fractions with the same denominator: Subtracting fractions with the same denominator:

1.1 Fractions To add or subtract fractions with different denominators - get a common denominator. Using the least common denominator: Factor both denominators completely Multiply the largest number of repeats of each prime factor together to get the LCD Multiply the top and bottom of each fraction by the number that produces the LCD in the denominator

1.1 Fractions Adding fractions with different denominators: Subtracting fractions with different denominators:

1.1 Fractions Try these:

1.2 Exponents and Order of Operations Note:

1.2 Exponents and Order of Operations PEMDAS (Please Excuse My Dear Aunt Sally) Parenthesis Exponentiation Multiplication / Division (evaluate left to right) Addition / Subtraction (evaluate left to right) Note: the fraction bar implies parenthesis

1.3 Geometry Review Acute angle – 0 < x < 90 Right angle - 90 Obtuse angle – 90 < x < 180 Straight angle - 180

1.3 Geometry Review Complementary angles – add up to 90 Supplementary angles – add up to 180 Vertical angles – the angles opposite each other are congruent

1.3 Geometry Review 1 2 3 4 5 6 7 8 When 2 parallel lines are cut by a transversal the following congruent pairs of angles are formed: Corresponding angles:1 & 5, 2 & 6, 3 & 7, 4 & 8 Alternate interior angles: 4 & 5, 3 & 6 Alternate exterior angles: 1 & 8, 2 & 7

1.3 Geometry Review 1 2 3 4 5 6 7 8 When 2 parallel lines are cut by a transversal the following supplementary pairs of angles are formed: Same side interior angles: 3 & 5, 4 & 6 Same side exterior angles: 1 & 7, 2 & 8

1.3 Geometry Review Terminology: Corresponding angles – in the same relative “quadrant” (upper right, lower left, etc.) Alternate – on opposite sides of the transversal Same side – on the same side of the transversal Interior – in between the 2 parallel lines Exterior – outside the 2 parallel lines

1.3 Geometry Review What type of angles are: 1 & 8 4 & 6 4 & 5 2 3 4 5 6 7 8 What type of angles are: 1 & 8 4 & 6 4 & 5 2 & 6 1 & 7

1.3 Geometry Review Triangles classified by number of congruent sides Types of triangles # sides congruent scalene isosceles 2 equilateral 3

1.3 Geometry Review Triangles classified by angles Types of triangles acute All angles acute obtuse One obtuse angle right One right angle equiangular All angles congruent

1.3 Geometry Review In a triangle, the sum of the interior angle measures is 180º (mA + mB + mC = 180º) A B C

1.3 Geometry Review Figure Area Square s2 Rectangle l  w Parallelogram b  h Triangle ½ (b  h) Trapezoid Circle

1.4 Sets of Numbers and Absolute Value Classifications of Numbers Natural numbers {1,2,3,…} Whole numbers {0,1,2,3,…} Integers {…-2,-1,0,1,2,…} Rational numbers – can be expressed as where p and q are integers -1.3, 2, 5.3147, Irrational numbers – not rational

1.4 Sets of Numbers and Absolute Value The real number line: Real numbers: {xx is a rational or an irrational number} -3 -2 -1 1 2 3

1.4 Sets of Numbers and Absolute Value Ordering of Real Numbers: a < b  a is to the left of b on the number line a > b  a is to the right of b on the number line Additive inverse of a number x: -x is a number that is the same distance from 0 but on the opposite side of 0 on the number line

1.4 Sets of Numbers and Absolute Value Double negative rule: -(-x) = x Absolute Value of a number x: the distance from 0 on the number line or alternatively How is this possible if the absolute value of a number is never negative?

1.5 Adding and Subtracting Real Numbers Adding numbers on the number line (2 + 2): -4 -3 -2 -1 1 2 3 4 2 2

1.5 Adding and Subtracting Real Numbers Adding numbers on the number line (-2 + -2): -4 -3 -2 -1 1 2 3 4 -2 -2

1.5 Adding and Subtracting Real Numbers Adding numbers with the same sign: Add the absolute values and use the sign of both numbers Adding numbers with different signs: Subtract the absolute values and use the sign of the number with the larger absolute value

1.5 Adding and Subtracting Real Numbers Subtraction: To subtract signed numbers: Change the subtraction to adding the number with the opposite sign

1.6 Multiplying and Dividing Real Numbers Multiplication by zero: For any number x, Multiplying numbers with different signs: For any positive numbers x and y, Multiplying two negative numbers: For any positive numbers x and y,

1.6 Multiplying and Dividing Real Numbers Reciprocal or multiplicative inverse: If xy = 1, then x and y are reciprocals of each other. (example: 2 and ½ ) Division is the same as multiplying by the reciprocal:

1.6 Multiplying and Dividing Real Numbers Division by zero: For any number x, Dividing numbers with different signs: For any positive numbers x and y, Dividing two negative numbers: For any positive numbers x and y,

1.7 Algebraic Expressions and Properties of Real Numbers x is a variable 5 is a coefficient 7 is a constant Evaluating an expression: substitute a value for the variable and evaluate example:the last expression when x=1

1.7 Algebraic Expressions and Properties of Real Numbers Commutative property (addition/multiplication) Associative property (addition/multiplication)

1.7 Algebraic Expressions and Properties of Real Numbers Identity property (addition/multiplication) Inverse property (addition/multiplication) Distributive property