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Fractions Review: Reducing Fractions (page 1 of 5)

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

In what follows, it will sometimes be useful to remember that fractions can indicate division. For instance, 1/3can mean "one divided by three", as well as "one part out of three parts".

You know that any number, divided by itself, is just 1. You use this fact when you reduce fractions. Here's how you would reduce 4/8:   Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved

    4/8 = (1/2)*(4/4) = (1/2)*(1) = 1/2

Note how I switched from a fraction with products (in the numerator and denominator) to a product of fractions. This switch is okay as long as you're multiplying, but NOT if you're adding. For instance:

    [ 1 + 4 ] / [ 2 + 4 ] does not equal 1/2 + 4/4

Just remember: For fractions, multiplying is way easier than adding. Now, to get back to business...




In addition to the canceling method I used above, you may also have seen either of the following "shorthands" for cancelation:



Any of these formats is fine. The last two are probably simplest for your handwritten homework; the first one is easier for typesetting.

If you have a regular (scientific, business, etc.) calculator that can handle fractions, then you can enter the fraction and then hit the "equals" button to get the reduced fraction. If you have a graphing calculator with a fraction command, then you can enter the fraction as a division (because 4/8 means "four divided by eight"), and then convert to fraction form. Check your manual. If your calculator can't handle fractions, or if the denominator is too large for the calculator to handle, here's how you do the reduction by hand.

  • Reduce 2940/3150 to simplest form.

    I'll grab my calculator and some scrap paper, and factor the numerator (top number) and denominator (bottom number). A quick shorthand for getting the prime factorization of each of these numbers is this:

      factorization of 2940

    (To find the factorization, I just read off the prime factors from around the outside of the upside-down division. From the above, I can see that 2940 factors as 2×2×3×5×7×7.)

      factorization of 3150

    Now I can reduce the fraction by canceling off the common factors:

      2940/3150 = [ 2·2·3·5·7·7 ] / [ 2·3·3·5·5·7 ] = [ 2·7 ] / [ 3·5 ] = 14/15

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Cite this article as:

Stapel, Elizabeth. "Fractions Review: Reducing Fractions." Purplemath. Available from Accessed



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