Operations with rational numbers
Keywords:
$$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$$

Addition 
$$\frac{a}{b}\frac{c}{d}=\frac{adbc}{bd}$$

Subtraction 
$$\frac{a}{b}\xb7\frac{c}{d}=\frac{ac}{bd}$$

Multiplication 
$$\frac{a}{b}:\frac{c}{d}=\frac{ad}{bc}$$

Division 