83/87 Additive Inverse :
The additive inverse of 83/87 is -83/87.
This means that when we add 83/87 and -83/87, the result is zero:
83/87 + (-83/87) = 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: 83/87
- Additive inverse: -83/87
To verify: 83/87 + (-83/87) = 0
Extended Mathematical Exploration of 83/87
Let's explore various mathematical operations and concepts related to 83/87 and its additive inverse -83/87.
Basic Operations and Properties
- Square of 83/87: 0.91015986259744
- Cube of 83/87: 0.86831343213319
- Square root of |83/87|: 0.97674100380078
- Reciprocal of 83/87: 1.0481927710843
- Double of 83/87: 1.9080459770115
- Half of 83/87: 0.47701149425287
- Absolute value of 83/87: 0.95402298850575
Trigonometric Functions
- Sine of 83/87: 0.81574902053315
- Cosine of 83/87: 0.57840602996443
- Tangent of 83/87: 1.4103397583585
Exponential and Logarithmic Functions
- e^83/87: 2.5961328917688
- Natural log of 83/87: -0.047067510857986
Floor and Ceiling Functions
- Floor of 83/87: 0
- Ceiling of 83/87: 1
Interesting Properties and Relationships
- The sum of 83/87 and its additive inverse (-83/87) is always 0.
- The product of 83/87 and its additive inverse is: -6889
- The average of 83/87 and its additive inverse is always 0.
- The distance between 83/87 and its additive inverse on a number line is: 166
Applications in Algebra
Consider the equation: x + 83/87 = 0
The solution to this equation is x = -83/87, which is the additive inverse of 83/87.
Graphical Representation
On a coordinate plane:
- The point (83/87, 0) is reflected across the y-axis to (-83/87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 83/87 and Its Additive Inverse
Consider the alternating series: 83/87 + (-83/87) + 83/87 + (-83/87) + ...
The sum of this series oscillates between 0 and 83/87, never converging unless 83/87 is 0.
In Number Theory
For integer values:
- If 83/87 is even, its additive inverse is also even.
- If 83/87 is odd, its additive inverse is also odd.
- The sum of the digits of 83/87 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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