Fractions Review: Multiplying and Dividing Fractions

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Fractions Review (page 3 of 5)

Sections: Reducing fractions, Mixed numbers and improper fractions, Multiplying and dividing fractions, Adding and subtracting fractions, Adding polynomial fractions

Multiplying fractions is easy: you multiply the top numbers and multiply the bottom numbers. For instance:

When possible, you reduce. In the example above, however, nothing reduces, because 8 and 45 have no factors in common. If you're not sure whether anything can be cancelled off, you can always factor the numerator and denominator, and check for any shared factors:

Often, though, something will cancel:

Simplify

( 4/9 )( 49/6 )( 27/8 ) = 7/2

Dividing fractions is just about as easy; there's just one extra step. When you divide by a fraction, the first thing you do is "flip-n-multiply". That is, you take the second fraction, flip it upside-down ("find the reciprocal"), and multiply the first fraction by this flipped fraction.