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Use the Properties of Proportions to Simplify Fractions

Part of the Algebra II Workbook For Dummies Cheat Sheet

The properties of proportions come in useful when solving equations involving fractions. When you can, change an equation with fractions in it to a proportion for ease in solving.

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

image1.png

is a proportion. Both fractions in that proportion reduce to

image2.png

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 proportion

image3.png

the cross-products are equal: ad = bc.

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

image4.png

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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