Mathematics » Introducing Fractions » Multiply and Divide Fractions

Key Concepts

Key Concepts

  • Equivalent Fractions Property
    • If \(a,b,c\) are numbers where \(b\ne 0\), \(c\ne 0\), then \(\frac{a}{b}=\frac{a\cdot c}{b\cdot c}\) and \(\frac{a\cdot c}{b\cdot c}=\frac{a}{b}\).
  • Simplify a fraction.
    1. Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.
    2. Simplify, using the equivalent fractions property, by removing common factors.
    3. Multiply any remaining factors.
  • Fraction Multiplication
    • If \(a,b,c,\) and \(d\) are numbers where \(b\ne 0\)and \(d\ne 0\), then \(\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}\).
  • Reciprocal
    • A number and its reciprocal have a product of \(1\). \(\frac{a}{b}\cdot \frac{b}{a}=1\)
      OppositeAbsolute ValueReciprocal
      has opposite signis never negativehas same sign, fraction inverts
  • Fraction Division
    • If \(a,b,c,\) and \(d\) are numbers where \(b\ne 0\), \(c\ne 0\) and \(d\ne 0\) , then
      \(\frac{a}{b}+\frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}\)

    • To divide fractions, multiply the first fraction by the reciprocal of the second



The reciprocal of the fraction \(\frac{a}{b}\) is \(\frac{b}{a}\) where \(a\ne 0\) and \(b\ne 0\).

simplified fraction

A fraction is considered simplified if there are no common factors in the numerator and denominator.

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