68/83 Additive Inverse :
The additive inverse of 68/83 is -68/83.
This means that when we add 68/83 and -68/83, the result is zero:
68/83 + (-68/83) = 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: 68/83
- Additive inverse: -68/83
To verify: 68/83 + (-68/83) = 0
Extended Mathematical Exploration of 68/83
Let's explore various mathematical operations and concepts related to 68/83 and its additive inverse -68/83.
Basic Operations and Properties
- Square of 68/83: 0.67121498040354
- Cube of 68/83: 0.54991106828242
- Square root of |68/83|: 0.9051392757105
- Reciprocal of 68/83: 1.2205882352941
- Double of 68/83: 1.6385542168675
- Half of 68/83: 0.40963855421687
- Absolute value of 68/83: 0.81927710843373
Trigonometric Functions
- Sine of 68/83: 0.73065246677453
- Cosine of 68/83: 0.68274956814068
- Tangent of 68/83: 1.0701617413897
Exponential and Logarithmic Functions
- e^68/83: 2.2688591054558
- Natural log of 68/83: -0.19933290262049
Floor and Ceiling Functions
- Floor of 68/83: 0
- Ceiling of 68/83: 1
Interesting Properties and Relationships
- The sum of 68/83 and its additive inverse (-68/83) is always 0.
- The product of 68/83 and its additive inverse is: -4624
- The average of 68/83 and its additive inverse is always 0.
- The distance between 68/83 and its additive inverse on a number line is: 136
Applications in Algebra
Consider the equation: x + 68/83 = 0
The solution to this equation is x = -68/83, which is the additive inverse of 68/83.
Graphical Representation
On a coordinate plane:
- The point (68/83, 0) is reflected across the y-axis to (-68/83, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 68/83 and Its Additive Inverse
Consider the alternating series: 68/83 + (-68/83) + 68/83 + (-68/83) + ...
The sum of this series oscillates between 0 and 68/83, never converging unless 68/83 is 0.
In Number Theory
For integer values:
- If 68/83 is even, its additive inverse is also even.
- If 68/83 is odd, its additive inverse is also odd.
- The sum of the digits of 68/83 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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