87/97 Additive Inverse :
The additive inverse of 87/97 is -87/97.
This means that when we add 87/97 and -87/97, the result is zero:
87/97 + (-87/97) = 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: 87/97
- Additive inverse: -87/97
To verify: 87/97 + (-87/97) = 0
Extended Mathematical Exploration of 87/97
Let's explore various mathematical operations and concepts related to 87/97 and its additive inverse -87/97.
Basic Operations and Properties
- Square of 87/97: 0.80444255500053
- Cube of 87/97: 0.72151033283553
- Square root of |87/97|: 0.94705185523014
- Reciprocal of 87/97: 1.1149425287356
- Double of 87/97: 1.7938144329897
- Half of 87/97: 0.44845360824742
- Absolute value of 87/97: 0.89690721649485
Trigonometric Functions
- Sine of 87/97: 0.78140066125657
- Cosine of 87/97: 0.62402965201006
- Tangent of 87/97: 1.2521851465545
Exponential and Logarithmic Functions
- e^87/97: 2.4520078425405
- Natural log of 87/97: -0.1088028598488
Floor and Ceiling Functions
- Floor of 87/97: 0
- Ceiling of 87/97: 1
Interesting Properties and Relationships
- The sum of 87/97 and its additive inverse (-87/97) is always 0.
- The product of 87/97 and its additive inverse is: -7569
- The average of 87/97 and its additive inverse is always 0.
- The distance between 87/97 and its additive inverse on a number line is: 174
Applications in Algebra
Consider the equation: x + 87/97 = 0
The solution to this equation is x = -87/97, which is the additive inverse of 87/97.
Graphical Representation
On a coordinate plane:
- The point (87/97, 0) is reflected across the y-axis to (-87/97, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 87/97 and Its Additive Inverse
Consider the alternating series: 87/97 + (-87/97) + 87/97 + (-87/97) + ...
The sum of this series oscillates between 0 and 87/97, never converging unless 87/97 is 0.
In Number Theory
For integer values:
- If 87/97 is even, its additive inverse is also even.
- If 87/97 is odd, its additive inverse is also odd.
- The sum of the digits of 87/97 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: