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.
 Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.
 Simplify, using the equivalent fractions property, by removing common factors.
 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 \(1\). \(\frac{a}{b}\cdot \frac{b}{a}=1\)

Opposite Absolute Value Reciprocal has opposite sign is never negative has 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
 If \(a,b,c,\) and \(d\) are numbers where \(b\ne 0\), \(c\ne 0\) and \(d\ne 0\) , then
Glossary
reciprocal
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.