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Intermediate Algebra: Fractions, Real Numbers, and Inequalities

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Terms in this set (20)

  • How do you simplify a fraction?
    Cancel out common factors in the numerator and denominator.
  • What is the rule for multiplying fractions?
    Multiply across numerators and denominators, then reduce if possible.
  • How do you divide fractions?
    Flip the second fraction (take the reciprocal) and multiply.
  • How do you add or subtract fractions with different denominators?
    Find the least common denominator (LCD), convert fractions, then add or subtract numerators only.
  • What is the least common denominator (LCD) of 12 and 8?
    The LCD is 24.
  • How do you convert a mixed number to an improper fraction?
    Multiply the whole number by the denominator and add the numerator; place the result over the original denominator.
  • How do you convert an improper fraction to a mixed number?
    Divide the numerator by the denominator; the quotient is the whole number and the remainder is the numerator of the fraction.
  • What are natural numbers?
    Counting numbers starting from 1, 2, 3, 4, 5, ...
  • What are whole numbers?
    Natural numbers including zero: 0, 1, 2, 3, 4, 5, ...
  • What are integers?
    Whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...
  • What are rational numbers?
    Numbers that can be expressed as a quotient of two integers (fractions or decimals that terminate or repeat).
  • What are irrational numbers?
    Numbers that cannot be expressed as a fraction and have non-terminating, non-repeating decimals, such as pi.
  • What are real numbers?
    All rational and irrational numbers combined.
  • How is absolute value defined?
    The distance of a number from zero on the number line; always non-negative.
  • What does the inequality symbol '<' mean?
    Means 'less than'; the value on the left is smaller than the value on the right.
  • What does the inequality symbol '>' mean?
    Means 'greater than'; the value on the left is larger than the value on the right.
  • What does the inequality symbol '≤' mean?
    Means 'less than or equal to'; the value on the left is smaller than or equal to the value on the right.
  • What does the inequality symbol '≥' mean?
    Means 'greater than or equal to'; the value on the left is larger than or equal to the value on the right.
  • How do you compare absolute values of numbers?
    Compare their distances from zero regardless of sign.
  • How do you add fractions with unlike denominators?
    Find the LCD, convert each fraction, then add the numerators.