63/71 Additive Inverse :
The additive inverse of 63/71 is -63/71.
This means that when we add 63/71 and -63/71, the result is zero:
63/71 + (-63/71) = 0
Additive Inverse of a Fraction
For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:
- Original fraction: 63/71
- Additive inverse: -63/71
To verify: 63/71 + (-63/71) = 0
Extended Mathematical Exploration of 63/71
Let's explore various mathematical operations and concepts related to 63/71 and its additive inverse -63/71.
Basic Operations and Properties
- Square of 63/71: 0.78734378099583
- Cube of 63/71: 0.69862898877095
- Square root of |63/71|: 0.94197873843414
- Reciprocal of 63/71: 1.1269841269841
- Double of 63/71: 1.7746478873239
- Half of 63/71: 0.44366197183099
- Absolute value of 63/71: 0.88732394366197
Trigonometric Functions
- Sine of 63/71: 0.77538462508266
- Cosine of 63/71: 0.63148925817105
- Tangent of 63/71: 1.2278666898125
Exponential and Logarithmic Functions
- e^63/71: 2.4286218186996
- Natural log of 63/71: -0.11954515064978
Floor and Ceiling Functions
- Floor of 63/71: 0
- Ceiling of 63/71: 1
Interesting Properties and Relationships
- The sum of 63/71 and its additive inverse (-63/71) is always 0.
- The product of 63/71 and its additive inverse is: -3969
- The average of 63/71 and its additive inverse is always 0.
- The distance between 63/71 and its additive inverse on a number line is: 126
Applications in Algebra
Consider the equation: x + 63/71 = 0
The solution to this equation is x = -63/71, which is the additive inverse of 63/71.
Graphical Representation
On a coordinate plane:
- The point (63/71, 0) is reflected across the y-axis to (-63/71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 63/71 and Its Additive Inverse
Consider the alternating series: 63/71 + (-63/71) + 63/71 + (-63/71) + ...
The sum of this series oscillates between 0 and 63/71, never converging unless 63/71 is 0.
In Number Theory
For integer values:
- If 63/71 is even, its additive inverse is also even.
- If 63/71 is odd, its additive inverse is also odd.
- The sum of the digits of 63/71 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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