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Calculating the square of a fraction is a fundamental operation in mathematics that allows us to find the area of a square whose side is represented by the fraction. Understanding how to perform this calculation is essential for various mathematical applications, including geometry, algebra, and problem-solving. By following a few simple steps, we can easily determine the square of a fraction and gain a deeper understanding of the relationship between fractions and their squares. In this article, we will explore the process of calculating the square of a fraction and examine its significance in mathematical contexts.
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Squaring fractions is one of the simplest calculations performed on fractions. Very similar to squaring integers, meaning you just multiply the numerator and denominator by itself. [1] X Research Source In some cases you have to reduce fractions before squaring to make the problem simpler. If you have not yet learned this skill, the following article will help you quickly understand the problem through an easy-to-understand overview.
Steps
Calculate the square of the fraction
- 5 2 = 5 × 5 = 25
- ( 5 / 2 ) 2 = 5 / 2 × 5 / 2 or ( 5 2 / 2 2 ).
- Square each number will give the result ( 25 / 4 ).
- The numerator is the term above the fraction, the denominator is the term below the fraction.
- For example: ( 5 / 2 ) 2 = ( 5 x 5 / 2 x 2 ) = ( 25 / 4 ).
- To convert to a mixed number, we divide 25 by 4 and get 6 times (6 x 4 = 24), odd 1. So the mixed number is 6 1 / 4 .
Calculating the square of a negative fraction
- Example: (– 2 / 4 )
- For example: (– 2 / 4 ) 2 = (– 2 / 4 ) x (– 2 / 4 )
- Example: (-2) x (-8) = (+16)
- Continuing with the above example, the fraction received will be a positive number.
- (– 2 / 4 ) x (– 2 / 4 ) = (+ 4 / 16 )
- By convention, the “+” before a positive number is omitted. [8] X Research Sources
- For example, ( 4 / 16 ) has a common factor of four.
- Divide numerator and denominator by 4: 4/4 = 1, 16/4= 4
- The fraction has been reduced to: ( 1 / 4 )
Use short and quick calculation
- Example: ( 12 / 16 ) 2
- 12 and 16 are both divisible by 4. 12/4 = 3 and 16/4 = 4; so 12/16 can be reduced to3/4.
- Now you will square the fraction 3 / 4 .
- ( 3 / 4 ) 2 = 9 / 16 , which can no longer be reduced.
- To prove this, square the original fraction without reduction:
- ( 12 / 16 ) 2 = ( 12 x 12 / 16 x 16 ) = ( 144 / 256 )
- ( 144 / 256 ) has a common factor of 16. Dividing both numerator and denominator by 16 reduces the fraction to ( 9 / 16 ), which is the same result we get when we reduce the original fraction first. .
- Example: 16 × ( 12 / 16 ) 2
- Solve the squared number and cancel the common factor 16:
16* 12 /16* 12 / 16- Since there is an integer 16 and two 16s in the denominator, you can cross out ONE of the two 16s in the denominator.
- Rewrite the reduced equation: 12 × 12 / 16
- Simplify 12/16 by dividing by4 : 3/4
- Multiply: 12 × 3 / 4 = 36/4
- Divide: 36/4 = 9
- Example: 16 * ( 12 / 16 ) 2
- Rewrite the expression as the square of the numerator and denominator: 16 * ( 12 2 / 16 2 )
- Suppress the exponent in the denominator:
16* 12 2 / 162- Imagine the first 16 has an exponent of 1:16 1 . Using the exponent rule in division, you subtract two exponents from each other. 16 1 /16 2 , resulting in 16 1-2 = 16 -1 or 1/16.
- You now have: 122/16
- Rewrite and reduce the fraction: 12*12 / 16 = 12 * 3 / 4 .
- Multiply: 12 × 3 / 4 = 36/4
- Divide: 36/4 = 9
Things you need
- Paper or writing board
- Pencil/ballpoint pen (for writing on paper)
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 38,489 times.
Squaring fractions is one of the simplest calculations performed on fractions. Very similar to squaring integers, meaning you just multiply the numerator and denominator by itself. [1] X Research Source In some cases you have to reduce fractions before squaring to make the problem simpler. If you have not yet learned this skill, the following article will help you quickly understand the problem through an easy-to-understand overview.
In conclusion, calculating the square of a fraction is a straightforward process that can be accomplished by following a few simple steps. It is essential to remember that the square of a fraction is obtained by squaring both the numerator and the denominator separately. This results in a new fraction with the squared values as their respective numerators and denominators. It is crucial to simplify the fraction if possible, reducing any common factors between the numerator and denominator. By understanding these steps and practicing with examples, one can confidently calculate the square of any given fraction.
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