MTH212 Foundations of Elementary Math 2

Fun with Fractions.

MTH212
Notes on Fractions
Winter 2020

Chapter 5: Integers and Fractions

§ 5.2 Introduction to Fractions

Topics

  • Fraction terminology
    • `"numerator"/"denominator"`
    • 0 < proper fraction < 1
    • Improper fraction > 1
    • Mixed number `2 1/2`
  • Fraction Concepts (Representations)
    • Part of a whole area
      two-thirds as an area
    • Part of a whole group
      two-thirds as a group
    • Position on a number line
      the position two-thirds on a number line
    • Division
      two things cut into three groups
    • Ratio
      the ratio of green to red is 2 to 3
  • Equality of Fractions
    Simplifying fractions
    • Grouping with models

    • division with numerator and denominator

      `6/12=(2*3)/(2*6)=3/6`

    • factoring and the GCF
  • Simplyfying Fractions with Calculators
  • Common Denominators
    • LCM of denominators
    • Signs: `-2/3=(-2)/3=2/(-3)`
      since the quotient of dividing numbers of oposite sign is a negative number.
    • Test for Equality
      `a/b=c/d` if and only if `ad=bc`
  • Inequality, Fraction comparisons
    • equal
      `4/12=7/21`
    • less than
      `1/3<1/2`
    • greater than
      `3/4>7/10` since `3*10 > 7*4`
  • Density of fractions

    Zoom in on the interval from 1/4 to 1/3
  • Mixed numbers
    why `7/3 = 2 1/3`
  • Mental calculations
  • Approximations