A **ratio** expresses the relative size or magnitude of one [[quantity]] with respect to another. The ratio of two quantities $a$ and $b$ is written as $a:b$ or as the [[fraction]] $a/b$, where a is the [[numerator]] and b is the [[denominator]]. For example, the ratio of $2$ to $3$ can be written as $2:3$ or as the fraction $2/3$. Ratios can be simplified by [[dividing]] or scaling down both the numerator and denominator by their [[greatest common factor]]. For example, the ratio $6:8$ can be simplified by dividing both by 2 to get $3:4$, or it can be un-simplified by multiplying both by any number like 5 to get $30:40$. Scaling the numerator and denominator of one ratio, results in another one that is *equivalent*. Ratios that are equivalent are in *proportion* with each other. For example, $6:8::3:4$ is a proportion statement that says $6:8$ and $3:4$ are in proportion, and therefor equivalent For the fraction form, we say they are [[equality|equal]] if they are equivalent, such as $\frac{6}{8}=\frac{3}{4}$ Ratios and fractions are used extensively in [[Geometry]], [[Probability]], and [[Algebra]].