68/71 Additive Inverse :
The additive inverse of 68/71 is -68/71.
This means that when we add 68/71 and -68/71, the result is zero:
68/71 + (-68/71) = 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: 68/71
- Additive inverse: -68/71
To verify: 68/71 + (-68/71) = 0
Extended Mathematical Exploration of 68/71
Let's explore various mathematical operations and concepts related to 68/71 and its additive inverse -68/71.
Basic Operations and Properties
- Square of 68/71: 0.91727831779409
- Cube of 68/71: 0.87852007901406
- Square root of |68/71|: 0.97864522625579
- Reciprocal of 68/71: 1.0441176470588
- Double of 68/71: 1.9154929577465
- Half of 68/71: 0.47887323943662
- Absolute value of 68/71: 0.95774647887324
Trigonometric Functions
- Sine of 68/71: 0.81789704991675
- Cosine of 68/71: 0.57536459374685
- Tangent of 68/71: 1.4215282949381
Exponential and Logarithmic Functions
- e^68/71: 2.6058175868291
- Natural log of 68/71: -0.043172171865209
Floor and Ceiling Functions
- Floor of 68/71: 0
- Ceiling of 68/71: 1
Interesting Properties and Relationships
- The sum of 68/71 and its additive inverse (-68/71) is always 0.
- The product of 68/71 and its additive inverse is: -4624
- The average of 68/71 and its additive inverse is always 0.
- The distance between 68/71 and its additive inverse on a number line is: 136
Applications in Algebra
Consider the equation: x + 68/71 = 0
The solution to this equation is x = -68/71, which is the additive inverse of 68/71.
Graphical Representation
On a coordinate plane:
- The point (68/71, 0) is reflected across the y-axis to (-68/71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 68/71 and Its Additive Inverse
Consider the alternating series: 68/71 + (-68/71) + 68/71 + (-68/71) + ...
The sum of this series oscillates between 0 and 68/71, never converging unless 68/71 is 0.
In Number Theory
For integer values:
- If 68/71 is even, its additive inverse is also even.
- If 68/71 is odd, its additive inverse is also odd.
- The sum of the digits of 68/71 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: