Editing Addition (section)

=== Rational numbers (fractions) ===
{{main article|Field of fractions}}
Addition of [[rational number]]s involves the [[fraction]]s. The computation can be done by using the [[least common denominator]], but a conceptually simpler definition involves only integer addition and multiplication:
<math display="block"> \frac{a}{b} + \frac{c}{d} = \frac{ad+bc}{bd}.</math>
As an example, the sum <math display="inline">\frac 34 + \frac 18 = \frac{3 \times 8+4 \times 1}{4 \times 8} = \frac{24 + 4}{32} = \frac{28}{32} = \frac78</math>.

Addition of fractions is much simpler when the [[denominator]]s are the same; in this case, one can simply add the numerators while leaving the denominator the same:
<math display="block"> \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}, </math>
so <math display="inline">\frac 14 + \frac 24 = \frac{1 + 2}{4} = \frac 34</math>.{{sfnp|Cameron|Craig|2013|p=29}}

The commutativity and associativity of rational addition are easy consequences of the laws of integer arithmetic.<ref>The verifications are carried out in {{harvtxt|Enderton|1977|p=[http://books.google.com/books?id=JlR-Ehk35XkC&pg=PA104 104]}} and sketched for a general field of fractions over a commutative ring in {{harvtxt|Dummit|Foote|1999}}, p. 263.</ref>