Summary: Multiplying and Dividing Fractions
Key Concepts
- Equivalent Fractions Property
- If [latex]a,b,c[/latex] are numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] , then [latex]\frac{a}{b}=\frac{a\cdot c}{b\cdot c}[/latex] and [latex]\frac{a\cdot c}{b\cdot c}=\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]\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}[/latex] .
- Reciprocal
- A number and its reciprocal have a product of [latex]1[/latex] . [latex]\frac{a}{b}\cdot \frac{b}{a}=1[/latex]
Opposite Absolute Value Reciprocal has opposite sign is never negative has same sign, fraction inverts
- A number and its reciprocal have a product of [latex]1[/latex] . [latex]\frac{a}{b}\cdot \frac{b}{a}=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]\frac{a}{b}+\frac{c}{d}=\frac{a}{b}\cdot \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]\frac{a}{b}[/latex] is [latex]\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.
Licenses & Attributions
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].