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

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then the following are all true:

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A proportion is an equation involving two ratios (fractions) set equal to each other. The following equation is a proportion:

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Both fractions in that proportion reduce to

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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,

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the cross-products are equal: a d = b c.

The reciprocals are equal (you can flip the fractions):

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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.)