67/81 Additive Inverse :
The additive inverse of 67/81 is -67/81.
This means that when we add 67/81 and -67/81, the result is zero:
67/81 + (-67/81) = 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: 67/81
- Additive inverse: -67/81
To verify: 67/81 + (-67/81) = 0
Extended Mathematical Exploration of 67/81
Let's explore various mathematical operations and concepts related to 67/81 and its additive inverse -67/81.
Basic Operations and Properties
- Square of 67/81: 0.68419448254839
- Cube of 67/81: 0.56593864605855
- Square root of |67/81|: 0.90948364131916
- Reciprocal of 67/81: 1.2089552238806
- Double of 67/81: 1.6543209876543
- Half of 67/81: 0.41358024691358
- Absolute value of 67/81: 0.82716049382716
Trigonometric Functions
- Sine of 67/81: 0.73601208490568
- Cosine of 67/81: 0.6769683972482
- Tangent of 67/81: 1.0872177902211
Exponential and Logarithmic Functions
- e^67/81: 2.2868160840802
- Natural log of 67/81: -0.18975653528147
Floor and Ceiling Functions
- Floor of 67/81: 0
- Ceiling of 67/81: 1
Interesting Properties and Relationships
- The sum of 67/81 and its additive inverse (-67/81) is always 0.
- The product of 67/81 and its additive inverse is: -4489
- The average of 67/81 and its additive inverse is always 0.
- The distance between 67/81 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/81 = 0
The solution to this equation is x = -67/81, which is the additive inverse of 67/81.
Graphical Representation
On a coordinate plane:
- The point (67/81, 0) is reflected across the y-axis to (-67/81, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/81 and Its Additive Inverse
Consider the alternating series: 67/81 + (-67/81) + 67/81 + (-67/81) + ...
The sum of this series oscillates between 0 and 67/81, never converging unless 67/81 is 0.
In Number Theory
For integer values:
- If 67/81 is even, its additive inverse is also even.
- If 67/81 is odd, its additive inverse is also odd.
- The sum of the digits of 67/81 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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