In algebra, the properties of proportions come in handy when solving equations involving fractions. When you can, change an algebraic equation with fractions in it to a proportion for easy solving.
If
then the following are all true:
A proportion is an equation involving two ratios (fractions) set equal to each other. The following equation is a proportion:
Both fractions in that proportion reduce to
so it's fairly easy to see how this statement is true.
Proportions have some interesting, helpful, and easy-to-use properties. For example, in the following proportion,
the cross-products are equal: a ∙ d = b ∙ c.
The reciprocals are equal (you can flip the fractions):
You can reduce the fractions vertically or horizontally: You can divide out factors that are common to both numerators or both denominators or the left fraction or the right fraction. (You can't, however, divide out a factor from the numerator of one fraction and the denominator of the other.)