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]\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]
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]\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+\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.
