If [latex]a,b,c[/latex] are numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] , then [latex]\Large\frac{a}{b}\normalsize=\Large\frac{a\cdot c}{b\cdot c}[/latex] and [latex]\Large\frac{a\cdot c}{b\cdot c}\normalsize=\Large\frac{a}{b}[/latex] .
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 [latex]a,b,c[/latex], and [latex]d[/latex] are numbers where [latex]b\ne 0[/latex] and [latex]d\ne 0[/latex] , then [latex]\Large\frac{a}{b}\cdot \frac{c}{d}\normalsize=\Large\frac{ac}{bd}[/latex] .
Reciprocal
A number and its reciprocal have a product of [latex]1[/latex] . [latex]\Large\frac{a}{b}\cdot \frac{b}{a}\normalsize=1[/latex]
Fraction Division
If [latex]a,b,c[/latex], and [latex]d[/latex] are numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] and [latex]d\ne 0[/latex] , then[latex]\Large\frac{a}{b}\normalsize\div\Large\frac{c}{d}\normalsize=\Large\frac{a}{b}\cdot\Large\frac{d}{c}[/latex]
To divide fractions, multiply the first fraction by the reciprocal of the second.
Glossary
reciprocal
The reciprocal of the fraction [latex]\Large\frac{a}{b}[/latex] is [latex]\Large\frac{b}{a}[/latex] where [latex]a\ne 0[/latex] and [latex]b\ne 0[/latex] .
simplified fraction
A fraction is considered simplified if there are no common factors in the numerator and denominator.
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Prealgebra. Provided by: OpenStax. License: CC BY: Attribution. License Terms: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757