Fractions

Summary

• \(a^{-1}⋅a=1\)
• \(a^{-1}\) and \( \frac{1}{a}\) different s ymbols for the same number
• \( \frac{a}{b}=a⋅ \frac{1}{b}=a⋅b^{-1}\)
• \( \frac{a}{b}\) and \(a/b\) are different n otation for \(a\) divided by \(b\)
• If \(a,b≠0\) are integers then \(a/b\) is called a common fraction
• \(b⋅ \frac{a}{b}=a\)
• \( \frac{a}{1}=a\)
• \( \frac{a}{a}=1 \)
• \( \frac{a}{b}⋅ \frac{c}{d}= \frac{a⋅c}{b⋅d}\)
• \( \frac{a}{b}= \frac{a⋅c}{b⋅c}\)
• \( \frac{a}{b}+ \frac{c}{b}= \frac{a+c}{b}\)
• \( \frac{-a}{b}= \frac{a}{-b}=- \frac{a}{b}\)
• \( \frac{-a}{-b}= \frac{a}{b}\)
• \( \frac{a/b}{c/d}= \frac{a}{b}⋅ \frac{d}{c}= \frac{ad}{bc}\)
• \( \frac{a}{b}+ \frac{c}{d}= \frac{ad+bc}{bd}\)