65/67 Additive Inverse :
The additive inverse of 65/67 is -65/67.
This means that when we add 65/67 and -65/67, the result is zero:
65/67 + (-65/67) = 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: 65/67
- Additive inverse: -65/67
To verify: 65/67 + (-65/67) = 0
Extended Mathematical Exploration of 65/67
Let's explore various mathematical operations and concepts related to 65/67 and its additive inverse -65/67.
Basic Operations and Properties
- Square of 65/67: 0.94118957451548
- Cube of 65/67: 0.91309436333592
- Square root of |65/67|: 0.98496154936695
- Reciprocal of 65/67: 1.0307692307692
- Double of 65/67: 1.9402985074627
- Half of 65/67: 0.48507462686567
- Absolute value of 65/67: 0.97014925373134
Trigonometric Functions
- Sine of 65/67: 0.82497007721463
- Cosine of 65/67: 0.56517640759367
- Tangent of 65/67: 1.4596682843275
Exponential and Logarithmic Functions
- e^65/67: 2.6383382117916
- Natural log of 65/67: -0.030305349495329
Floor and Ceiling Functions
- Floor of 65/67: 0
- Ceiling of 65/67: 1
Interesting Properties and Relationships
- The sum of 65/67 and its additive inverse (-65/67) is always 0.
- The product of 65/67 and its additive inverse is: -4225
- The average of 65/67 and its additive inverse is always 0.
- The distance between 65/67 and its additive inverse on a number line is: 130
Applications in Algebra
Consider the equation: x + 65/67 = 0
The solution to this equation is x = -65/67, which is the additive inverse of 65/67.
Graphical Representation
On a coordinate plane:
- The point (65/67, 0) is reflected across the y-axis to (-65/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 65/67 and Its Additive Inverse
Consider the alternating series: 65/67 + (-65/67) + 65/67 + (-65/67) + ...
The sum of this series oscillates between 0 and 65/67, never converging unless 65/67 is 0.
In Number Theory
For integer values:
- If 65/67 is even, its additive inverse is also even.
- If 65/67 is odd, its additive inverse is also odd.
- The sum of the digits of 65/67 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: