Math‎ > ‎

Math Study Guide


Integers

Whole Numbers


Integers 

Number Line 

Compare Integers 

To compare numbers, you can draw or imagine where both of the numbers are on the number line. The number that is closest to +∞ (the right) is "greater", and the number that is closest to ‐∞ (the left) is "less". If both numbers have the same value (the same place on the number line) they are "equal".


Absolute Value
The absolute value of a number is that number’s distance from zero. The answer is always positive or zero because we never measure distance with negative numbers.

   examples:

a. |37|represents the absolute value of 37. |37| = 37 because the distance between the number 37 and 0 is 37.

   

b. |-­0.87| = 0.87 represents the absolute value of -0.87. |-0.87| = 0.87 because the distance between the number -0.87 and 0 is 0.87.

  

c.  |0| = 0  represents the absolute value of 0. |0| = 0 because the distance between the number 0 and 0 is 0.

  

  

  

Operations

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Properties of Numbers
  • Order of Operations

Exponents

  • Exponents & Powers
  • Rules of Exponents

Multiples & Factors

  • Least Common Multiple
  • Greatest Common Factor
  • Prime & Composite Numbers

Fractions

  • What is a Fraction?
  • Equivalent Fractions
  • Simplifying Fractions
  • Common Denominators
  • Comparing Fractions
  • Improper Fractions & Mixed Numbers

Operations with Fractions

  • Add and Subtract Fractions
  • Multiply Fractions
  • Reciprocals
  • Divide Fractions

Decimals

  • Place Value
  • Convert Fractions to Decimals
  • Add & Subtract Decimals
  • Multiply & Divide Decimals
  • Terminating & Repeating Decimals
  • Convert Decimals to Fractions

Ratios

  • What is a Ratio?
  • Write Ratios as Fractions
  • Compare Ratios
  • Unite Rates
  • Solve Proportions
  • Read Scale Drawings & Models
  • Problems with Average Speed, Distance, Time

Percents

  • What is a Percent?
  • Write Percents as Decimals & Fractions
  • Find the Percent of a Number
  • Find the Percent when Given 2 Numbers
  • Percent Increase/Decrease
  • Discounts, Markups, Commission, and Profit
  • Simple and Compound Interest

Expressions

  • What is a Variable?
  • Write an Expression from a Verbal Description
  • Simplify Expressions
  • Evaluate Expressions

Equations

  • What is an Equation?
  • Solve One-Step Equations
  • Guess and Check
  • Undoing
  • Solve Two-Step Equations

Inequalities

  • Write an Inequality from a Verbal Description
  • Solve Inequalities

Linear Equations

  • The Coordinate Plane
  • Generate a Table & Graph from an Equation
  • Use Equations, Tables & Graphs to Solve Problems
  • Slope
  • y-intercept
  • Slope-Intercept Form

Pythagorean Theorem

  • Squares and Square Roots
  • What is the Pythagorean Theorem?
  • Use the Pythagorean Theorem to Solve Problems
  • Converse of Pythagorean Theorem
  • Pythagorean Triples