Adding Fractions
Operation under which each pair [latex]\left( \frac {a} {b},\frac {c} {d}\right) [/latex] of fractions is made to correspond to a new fraction [latex]\frac {ad\space+\space bc} {bd}[/latex] called the sum of these fractions.
Generally, we calculate the sum of two fractions using this algorithm:
[latex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd} + \dfrac{bc}{bd}=\dfrac{ad+bc}{bd}[/latex]
Examples
- [latex]\dfrac {2} {5}+\dfrac {1} {6}= \dfrac{2x6}{5x6} +\dfrac{5x1}{5x6}=\dfrac{12}{30}+\dfrac{5}{30}=\dfrac{12+5}{30}=\dfrac{17}{30}[/latex]
- If the denominators are the same, then the addition occurs by adding the numerators : [latex]\dfrac {3} {7}+\dfrac {1} {7}=\dfrac {3+1} {7}=\dfrac {4} {7}[/latex]