How to Square Fractions

How to Square Fractions

Squaring fractions is one of the simplest operations you can
perform on fractions. If you haven't yet learned this skill,
this article provides an easy overview that will improve
your understanding quickly.

!! Steps !!

Consider how you square non-fractions. You multiply it by itself, as
shown in the following example:

* 52 = 5 * 5 = 25

Note that squaring fractions [1] works the same way. For example:

* ( 5/2 )2 = 5/2 * 5/2

* = ( 52/22 )

* = ( 25/4 )

Consider if you can reduce (simplify) the fraction before you
square it. For example:

* ( 12/16 )2

* 12/16 reduces to 3/4

* ( 12/16)2 = 144/256, which will simplify to 9/16 .
( 3/4 )2 = 9/16, which can not be reduced.

* It is *usually* easier to reduce fractions before squaring them.

Recognize when you should wait to reduce a fraction. If solving a
more complex equation [2], one of the factors could simply be
"canceled" out, so you should wait to reduce. Changing the example
above; adding an additional factor to the problem:

* 16 * (12/16)2

* 16 * 12/16 * 12/16 = Canceling out 16's

* 12 * 12/16 =

* 12 * 3/4 = 9 , 12/16 is now reduced to 3/4 and multiplied times
12.

Understand how to use a shortcut. Using the same example, remove
the 2. For example:

* 16 * ( 12/16 )2

* = 16 * ( 122/162)

* = *16* * 122/*162,* The factor 16 cancels out the exponent in the
denominator.

* = 122/16

* = 12*12/16 We can now reduce the fraction 12/16 to 3/4.

* = 12 * 3/4 = 9

* Keep an open mind [3]. Several methods may be used to get to the
same answer. The more complex an equation; the more options you
have.

!! Things You'll Need !!

* Paper or screen for working on

!! Related WikiHows !!

* How to Change a Common Fraction Into a Decimal [4]

* How to Convert Percents, Fractions, and Decimals [5]

* How to Convert a Mixed Fraction [6]

* How to Divide Fractions by a Whole Number [7]

* How to Divide Fractions by Fractions [8]

* How to Multiply Fractions [9]

* How to Count to 99 on Your Fingers [10]

!! Article Tools !!

* Read on wikiHow

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Links:
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[1] http://www.wikihow.com/Solve-Fraction-Questions-in-Math
[2] http://www.wikihow.com/Solve-Trigonometric-Equations
[3] http://www.wikihow.com/Exercise-an-Open-Mind
[4] http://www.wikihow.com/Change-a-Common-Fraction-Into-a-Decimal
[5] http://www.wikihow.com/Convert-Percents%2C-Fractions%2C-and-Decimals
[6] http://www.wikihow.com/Convert-a-Mixed-Fraction
[7] http://www.wikihow.com/Divide-Fractions-by-a-Whole-Number
[8] http://www.wikihow.com/Divide-Fractions-by-Fractions
[9] http://www.wikihow.com/Multiply-Fractions
[10] http://www.wikihow.com/Count-to-99-on-Your-Fingers