83/84 Additive Inverse :
The additive inverse of 83/84 is -83/84.
This means that when we add 83/84 and -83/84, the result is zero:
83/84 + (-83/84) = 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: 83/84
- Additive inverse: -83/84
To verify: 83/84 + (-83/84) = 0
Extended Mathematical Exploration of 83/84
Let's explore various mathematical operations and concepts related to 83/84 and its additive inverse -83/84.
Basic Operations and Properties
- Square of 83/84: 0.97633219954649
- Cube of 83/84: 0.96470919717093
- Square root of |83/84|: 0.994029797388
- Reciprocal of 83/84: 1.0120481927711
- Double of 83/84: 1.9761904761905
- Half of 83/84: 0.49404761904762
- Absolute value of 83/84: 0.98809523809524
Trigonometric Functions
- Sine of 83/84: 0.83497933908857
- Cosine of 83/84: 0.55028129469864
- Tangent of 83/84: 1.5173682026496
Exponential and Logarithmic Functions
- e^83/84: 2.6861131904093
- Natural log of 83/84: -0.011976191046716
Floor and Ceiling Functions
- Floor of 83/84: 0
- Ceiling of 83/84: 1
Interesting Properties and Relationships
- The sum of 83/84 and its additive inverse (-83/84) is always 0.
- The product of 83/84 and its additive inverse is: -6889
- The average of 83/84 and its additive inverse is always 0.
- The distance between 83/84 and its additive inverse on a number line is: 166
Applications in Algebra
Consider the equation: x + 83/84 = 0
The solution to this equation is x = -83/84, which is the additive inverse of 83/84.
Graphical Representation
On a coordinate plane:
- The point (83/84, 0) is reflected across the y-axis to (-83/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 83/84 and Its Additive Inverse
Consider the alternating series: 83/84 + (-83/84) + 83/84 + (-83/84) + ...
The sum of this series oscillates between 0 and 83/84, never converging unless 83/84 is 0.
In Number Theory
For integer values:
- If 83/84 is even, its additive inverse is also even.
- If 83/84 is odd, its additive inverse is also odd.
- The sum of the digits of 83/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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