A *ratio* is a relationship between two numbers (or two objects) that defines the quantity of the first in comparison to the second. For example, for most mammals the ratio of legs to noses is \( 4:1 \), but for humans, the ratio of legs to noses is \( 2:1 \). Ratios can also be written in fractional form, so comparing three boys with five girls could be written \( 3:5 \) or \( \frac{3}{5} \).

When two objects are *proportional*, it means that their ratios are equal. Specifically, two ratios, \( a:b \) and \( c:d \), are "in the same proportion" or "proportional" if and only if:

\[ a:b :: c:d \Leftrightarrow \frac{a}{b}=\frac{c}{d} \Leftrightarrow ad = bc \]

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