arithmetic

• Integers


  Includes zero and all positive and negative numbers with no fractional parts/decimals
• Whole Numbers


  Includes zero and positive integers
• Natural Numbers


  Includes all positive integers
• Rational Numbers


  Includes fractions, terminating decimals, non-terminating repeating decimals, and integers
• Irrational Numbers


  Includes numbers that cannot be expressed as a fraction, or when its decimal form is nonterminating and nonrepeating
• Addition - Same Sign


  To add a positive number with another positive number, or vice versa, simply add the numbers and retain their common sign
• Addition - Different Sign


  To add a positive and a negative number, simply subtract each other and retain the sign of the number with the greater absolute value
• Subtraction


  To perform subtraction involving negative numbers, simply remember the "Keep, change, change" rule: Keep the sign of the first number, change the sign of the operation, change the sign of the second number, then perform addition

  
• Multiplication and Division


  Perform the operation and retain the sign by the rule "even = positive sign; odd = negative sign." If one has multiplied or divided two or an even amount of negative integers, the result would be positive. If odd, it would be negative.
• PEMDAS Rule


  The order at decreasing priority: Parenthesis, Exponents, Multiplication / Division, Addition / Subtraction
• Greatest Common Factor (GCF)


  The largest factor common to two or more numbers; this can be acquired by multiplying all common prime factors during factorization
• Least Common Multiple (LCM)


  The smallest multiple common to two or more numbers; this can be acquired by multiplying all prime factors present to both, without exceeding the number of prime factors that have appeared during a factorization of a number
• Factorization


  Expressing a number into its factors, commonly its prime factors in a more specific method called prime factorization. The most common way of factorization is by listing the factors and continuous division.
• Divisibility Rules


  A number is divisible by certain rules based on its digits
• Divisibility Rules


  • 90 is divisible by 2, 3, 5, 6, 10, 15

  435,504 is divisible by 3, 9

  332 is divisible by 4

  25,000 is divisible by 5

  624 is divisible by 2, 3, 6, 12

  214,116 is divisible by 7

  1,000 is divisible by 8, 10

  76,491 is divisible by 9

  5,269 is divisible by 11

  649,416 is divisible by 3, 4, 12

  405 is divisible by 3, 5, 15
• Proper Fraction


  Its numerator is less than its denominator
• Improper Fraction


  Its numerator is greater than its denominator
• Mixed Number


  Has a whole number together with a proper fraction
• Decimal


  Parts of a whole that may be represented by fractions whose denominators are multiples of 10
• Percent


  Another way of expressing parts of a whole, but this time the denominator is always 100
• Ratio


  Another way of expressing division of two numbers for the purpose of comparison, in the form of x:y
• Proportion


  An equality of two ratios, written as x:y = a:b
• Types of Proportion


  • Direct Proportion / Direct Variation
  • Inverse Proportion / Inverse Variation
  • Joint Variation