Fractions Review (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, 1/3 can 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 2000-2007 All Rights Reserved

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

Note how I switched from a fraction with products 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:

cancelation

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.

Grab your 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

(Just read off the prime factors from around the outside of the upside-down division.)

factorization of 3150

Now you can reduce the fraction, by canceling off common factors:

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