82/87 Additive Inverse :
The additive inverse of 82/87 is -82/87.
This means that when we add 82/87 and -82/87, the result is zero:
82/87 + (-82/87) = 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: 82/87
- Additive inverse: -82/87
To verify: 82/87 + (-82/87) = 0
Extended Mathematical Exploration of 82/87
Let's explore various mathematical operations and concepts related to 82/87 and its additive inverse -82/87.
Basic Operations and Properties
- Square of 82/87: 0.8883604174924
- Cube of 82/87: 0.83730522108479
- Square root of |82/87|: 0.9708391914381
- Reciprocal of 82/87: 1.0609756097561
- Double of 82/87: 1.8850574712644
- Half of 82/87: 0.47126436781609
- Absolute value of 82/87: 0.94252873563218
Trigonometric Functions
- Sine of 82/87: 0.80904693484463
- Cosine of 82/87: 0.58774404056401
- Tangent of 82/87: 1.3765293716432
Exponential and Logarithmic Functions
- e^82/87: 2.5664631263686
- Natural log of 82/87: -0.059188871390331
Floor and Ceiling Functions
- Floor of 82/87: 0
- Ceiling of 82/87: 1
Interesting Properties and Relationships
- The sum of 82/87 and its additive inverse (-82/87) is always 0.
- The product of 82/87 and its additive inverse is: -6724
- The average of 82/87 and its additive inverse is always 0.
- The distance between 82/87 and its additive inverse on a number line is: 164
Applications in Algebra
Consider the equation: x + 82/87 = 0
The solution to this equation is x = -82/87, which is the additive inverse of 82/87.
Graphical Representation
On a coordinate plane:
- The point (82/87, 0) is reflected across the y-axis to (-82/87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 82/87 and Its Additive Inverse
Consider the alternating series: 82/87 + (-82/87) + 82/87 + (-82/87) + ...
The sum of this series oscillates between 0 and 82/87, never converging unless 82/87 is 0.
In Number Theory
For integer values:
- If 82/87 is even, its additive inverse is also even.
- If 82/87 is odd, its additive inverse is also odd.
- The sum of the digits of 82/87 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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