Use the Properties of Proportions to Simplify Fractions

Part of the Algebra II Workbook For Dummies Cheat Sheet

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.)

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