# How do you add rational numbers?

Now, if you want to add two fraction, you first of all transform both of them as just shown, obtaining two equivalent fractions with the same denominator. At this point, you have a sum of two fraction of the form $\setminus \frac{a}{b} + \setminus \frac{c}{b}$, which is easily $\setminus \frac{a + c}{b}$.
To do so, you look for the least common multiple of the two denominator. Let's say that we have to calculate $\setminus \frac{3}{5} + \setminus \frac{5}{8}$. The least common multiple of 5 and 8 is 40, so we have to transform $\setminus \frac{3}{5}$ into $\setminus \frac{24}{40}$ (multiplying numerator and denominator by 8), and then we transform $\setminus \frac{5}{8}$ into $\setminus \frac{25}{40}$ (multiplying numerator and denominator by 5).
These are equivalent fraction, so we can be sure that $\setminus \frac{3}{5} + \setminus \frac{5}{8}$ equals $\setminus \frac{24}{40} + \setminus \frac{25}{40}$. The advantage is, of course, that the second one is much easier to compute, since one immediately gets that $\setminus \frac{24}{40} + \setminus \frac{25}{40} = \setminus \frac{49}{40}$