67/82 Additive Inverse :
The additive inverse of 67/82 is -67/82.
This means that when we add 67/82 and -67/82, the result is zero:
67/82 + (-67/82) = 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: 67/82
- Additive inverse: -67/82
To verify: 67/82 + (-67/82) = 0
Extended Mathematical Exploration of 67/82
Let's explore various mathematical operations and concepts related to 67/82 and its additive inverse -67/82.
Basic Operations and Properties
- Square of 67/82: 0.66760856632957
- Cube of 67/82: 0.54548504809855
- Square root of |67/82|: 0.90392099805885
- Reciprocal of 67/82: 1.2238805970149
- Double of 67/82: 1.6341463414634
- Half of 67/82: 0.40853658536585
- Absolute value of 67/82: 0.81707317073171
Trigonometric Functions
- Sine of 67/82: 0.72914595596492
- Cosine of 67/82: 0.68435822118245
- Tangent of 67/82: 1.065444869947
Exponential and Logarithmic Functions
- e^67/82: 2.2638641875984
- Natural log of 67/82: -0.20202662787329
Floor and Ceiling Functions
- Floor of 67/82: 0
- Ceiling of 67/82: 1
Interesting Properties and Relationships
- The sum of 67/82 and its additive inverse (-67/82) is always 0.
- The product of 67/82 and its additive inverse is: -4489
- The average of 67/82 and its additive inverse is always 0.
- The distance between 67/82 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/82 = 0
The solution to this equation is x = -67/82, which is the additive inverse of 67/82.
Graphical Representation
On a coordinate plane:
- The point (67/82, 0) is reflected across the y-axis to (-67/82, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/82 and Its Additive Inverse
Consider the alternating series: 67/82 + (-67/82) + 67/82 + (-67/82) + ...
The sum of this series oscillates between 0 and 67/82, never converging unless 67/82 is 0.
In Number Theory
For integer values:
- If 67/82 is even, its additive inverse is also even.
- If 67/82 is odd, its additive inverse is also odd.
- The sum of the digits of 67/82 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: