1. 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

2. 1.1 Fractions
Multiplying fractions:
Dividing fractions:

3. 1.1 Fractions Adding fractions with the same denominator:
Subtracting fractions with the same denominator:

4. 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

5. 1.1 Fractions Adding fractions with different denominators:
Subtracting fractions with different denominators:

6. 1.1 Fractions
Try these:

7. 1.2 Exponents and Order of Operations
Note:

8. 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

9. 1.3 Geometry Review Acute angle – 0 < x < 90 Right angle - 90
Obtuse angle – 90 < x < 180
Straight angle - 180

10. 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

11. 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

12. 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

13. 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

14. 1.3 Geometry Review What type of angles are: 1 & 8 4 & 6 4 & 52 3 4 5 6 7 8
What type of angles are:
1 & 8
4 & 6
4 & 5
2 & 6
1 & 7

15. 1.3 Geometry Review Triangles classified by number of congruent sides
Types of triangles
# sides congruent
scalene
isosceles 2
equilateral 3

16. 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

17. 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

18. 1.3 Geometry Review Figure Area Square s2 Rectangle l  w
Parallelogram
b  h
Triangle
½ (b  h)
Trapezoid
Circle

19. 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, ,
Irrational numbers – not rational

20. 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

21. 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

22. 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?

23. 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

24. 1.5 Adding and Subtracting Real Numbers
Adding numbers on the number line ( ): -4 -3 -2 -1 1 2 3 4 -2 -2

25. 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

26. 1.5 Adding and Subtracting Real Numbers
Subtraction:
To subtract signed numbers: Change the subtraction to adding the number with the opposite sign

27. 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,

28. 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:

29. 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,

30. 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

31. 1.7 Algebraic Expressions and Properties of Real Numbers
Commutative property (addition/multiplication)
Associative property (addition/multiplication)

32. 1.7 Algebraic Expressions and Properties of Real Numbers
Identity property (addition/multiplication)
Inverse property (addition/multiplication)
Distributive property