Pre-Algebra – Quick Reference Sheet

Properties of Algebra The Cartesian Coordinate System
Addition Multiplication

The additive identity is 0
The multiplicative identity is 1
a \cdot 1 =a
Inverse The additive inverse of a is -a
If a \neq 0, the multiplicative inverse of a is \frac{1}{a}
Associative (a+b)+c=a+(b+c) (ab)c=a(bc)
Commutative a+b=b+a a \cdot b = b \cdot a
Distributive a(b+c)=ab+ac and a(b-c)=ab-ac

Property of Inequalities

When multiplying or dividing each side of an inequality by a positive number an equivalent inequality is produced.
2x<6 \rightarrow \frac{2x}{2} < \frac{6}{-2} \rightarrow > -3

When multiplying or dividing each side of an inequality by a negative number the equivalent inequality is produced by reversing the direction of the inequality.
2x<6 \rightarrow \frac{2x}{-2}<\frac{6}{-2} \rightarrow x >-3

Order of Operations (PENDAS)

  1. Parentheses
  2. Exponents
  3. Multiplication and Division
  4. Addition and Subtraction
The Cartesian plane contains two axis, the x-axis and y-axis. The coordinates of point are written (x,y). You can tell what quadrant a point lies in by the signs of the coordinate.
Quadrant 1: (+,+)
Quadrant 2:(-,+)
Quadrant 3:(-,-)
Quadrant 4:(+,-)


Probability: the likelihood that an event will occur
P(success)=\frac{# Possible\quad successes}{# Possible \quad outcomes}

Multiplication Rule: When there are multiple independent events happening together the individual probabilities are multiplied together. Such events are drawing two cards from a deck or flipping a coin.
Example:A coin flipped and a 6-sided die is rolled at the same time. What is the probability of getting heads and 3?
P(rolls\quad 3) = \frac{1}{6} and P(heads)=\frac{1}{2}
P(heads\quad and\quad rolls 3)=\frac{1}{6} \times \frac{1}{2}=\frac{1}{12}

Addition Rule: When there are two mutually exclusive events (outcomes cannot happen at the same time), add the two individual probabilities together.
Example: A bag of marbles contains 1 green, 3 red, and 2 blue marbles. One marble is drawn. What is the probability that it is either green or blue?
P(green)=\frac{1}{6} and P(blue)=\frac{2}{6}
P(green\quad and\quad blue) = \frac{1}{6}+\frac{2}{6}=\frac{3}{6}=\frac{1}{2}
Ratios and Percentages

Ratio: when two qualities are divided as a means of comparing them
Percentage: a fraction (or ration) out of 100
Converting From Fraction to a Percentage

To convert a fraction to a percentage first write the fraction as a decimal then multiply the decimal by 100 and add the percent symbol (%).

\frac{3}{5}=0.6 \times 100 = 60%
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