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Fractions Review: Multiplying & Dividing (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:

    ( 2/3 )( 4/15 ) = ( 2·4 ) / ( 3·15 ) = 8/45

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:

    8/45 = ( 2·2·2 ) / ( 3·3·5 )

Nothing cancels.   Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved

Often, though, something will cancel:

  • Simplify (4/9) * (49/6) * (27/28)

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


You can use the Mathway widget below to practice multiplying fractions. Try the entered exercise, type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)

(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free seven-day trial of the software.)


 

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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.

  • Simplify (3/5) / (9/4)

    (3/5) / (9/4) = (4/15)

  • Simplify (5/6) / 5

    (5/6) / 5 = (1/6)

  • Simplify (4 + 3/8) / (2 + 5/6)

    (4 + 3/8) / (2 + 5/6) = 1 + 37/68
     


You can use the Mathway widget below to practice dividing fractions. Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)

(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free seven-day trial of the software.)

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Cite this article as:

Stapel, Elizabeth. "Fractions Review: Multiplying and Dividing Fractions." Purplemath. Available from
    http://www.purplemath.com/modules/fraction3.htm. Accessed
 

 

 

 

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