Squaring fractions is among the simplest operations you deserve to perform top top fractions. The is very comparable to squaring whole numbers in that you merely multiply both the numerator and also the denominator through itself.

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<1> there are additionally some instances in which simple the portion before squaring provides the procedure easier. If friend haven"t yet learned this skill, this post provides straightforward overview that will enhance your expertise quickly.


Squaring Fractions

Understand exactly how to square entirety numbers. Once you see an exponent the two, you understand that you should square the number. To square a entirety number, you multiply it through itself.<2> because that example: 52 = 5 × 5 = 25Realize the squaring fractions works the very same way. To square a fraction, you main point the portion by itself. Another method to think about it is to main point the numerator by itself and then the denominator through itself.<1> because that example: (5/2)2 = 5/2 × 5/2 or (52/22). Squaring each number yields (25/4).Multiply the numerator by itself and also the denominator by itself. The yes, really order the you multiply these numbers by themselves doesn’t issue as long as you have squared both numbers. To save things simple, begin with the numerator: just multiply the by itself. Then, multiply the denominator by itself. The numerator will continue to be on optimal of the portion and the denominator will stay at the bottom that the fraction. because that example: (5/2)2 = (5 x 5/2 x 2) = (25/4).Simplify the fraction to finish. When working with fractions, the last step is constantly to reduce the fraction to its most simple form or revolve the rotate an Improper portion Into a combined Number.<3> for our example, 25/4 is an improper portion because the numerator is larger than the denominator. To convert to a blended number, division 4 into 25. It goes in 6 time (6 x 4 = 24) v 1 leftover. Therefore, the combined number is 6 1/4.

Squaring fractions with an adverse Numbers

Recognize the an adverse sign in prior of the fraction. If you space working v a an unfavorable fraction, it will have a minus authorize in prior of it. That is an excellent practice to constantly put parentheses roughly a negative number therefore you know that the “–“ sign is referring to the number and not telling you to subtract 2 numbers.<4> for example: (–2/4)Multiply the fraction by itself. Square the fraction as you would generally by multiply the molecule by itself and also then multiply the denominator by itself. Alternatively, you deserve to simply main point the portion by itself. Because that example: (–2/4)2 = (–2/4) x (–2/4)Understand that two negative numbers main point to make a confident number. As soon as a minus authorize is present, the entire portion is negative. When you square the fraction, you space multiplying two negative numbers together. At any time two negative numbers room multiplied together, they do a positive number.<4> because that example: (-2) x (-8) = (+16)Remove the negative sign after squaring. After you have squared the fraction, girlfriend will have actually multiplied two negative numbers together. This method that the squared portion will be positive. Be sure to create your last answer without the negative sign.

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<1> continuing the example, the resulting fraction will be a optimistic number. (–2/4) x (–2/4) = (+4/16)Reduce the fraction to its most basic form. The final step when doing any type of calculations through a fraction is to mitigate it. Improper fractions must an initial be simplified right into mixed numbers and also then reduced. For example: (4/16) has actually a usual factor of four. Division the portion through through 4: 4/4 = 1, 16/4= 4 Rewrite simplified fraction: (1/4)

Using Simplifications and also Shortcuts

Check to see if you can simplify the fraction before friend square it. The is usually much easier to minimize fractions before squaring them. Remember, to mitigate a portion means to division it through a typical factor till the number one is the only number that deserve to be evenly separated into both the numerator and denominator.<5> reduce the fraction an initial means girlfriend don’t have to reduce it in ~ the end when the numbers will certainly be larger. Because that example: (12/16)2 12 and also 16 can both be split by 4. 12/4 = 3 and 16/4 = 4; therefore, 12/16 reduces to 3/4. Now, you will certainly square the portion 3/4. (3/4)2 = 9/16, which can not be reduced. Come prove this, stop square the original portion without reducing: (12/16)2 = (12 x 12/16 x 16) = (144/256) (144/256) has actually a common factor that 16. Splitting both the numerator and denominator by 16 to reduce the fraction to (9/16), the same portion we acquired from reducing first. Learn to recognize when you must wait to alleviate a fraction. Once working v more complicated equations, friend may have the ability to simply cancel among the factors. In this case, it is actually easier to wait prior to you mitigate the fraction. Adding an additional factor to the over example illustrates this. For example: 16 × (12/16)2 expand out the square and also cross out the typical factor that 16: 16 * 12/16 * 12/16 since there is one 16 totality number and also two 16’s in the denominator, you have the right to cross among them out. Rewrite the simplified equation: 12 × 12/16 reduce 12/16 by dividing through by 4: 3/4 Multiply: 12 × 3/4 = 36/4 Divide: 36/4 = 9Understand exactly how to usage an exponent shortcut. Another way to resolve the same example is to leveling the exponent first. The end result is the same, it’s simply a different means to solve. Because that example: 16 * (12/16)2 Rewrite v the numerator and denominator squared: 16 * (122/162) Cancel out the exponent in the denominator: 16 * 122/162 Imagine the very first 16 has an exponent the 1: 161. Making use of the exponent rule of separating numbers, friend subtract the exponents. 161/162, yields 161-2 = 16-1 or 1/16. Now, you are working with: 122/16 Rewrite and also reduce the fraction: 12*12/16 = 12 * 3/4. Multiply: 12 × 3/4 = 36/4 Divide: 36/4 = 9