73/81 Additive Inverse :
The additive inverse of 73/81 is -73/81.
This means that when we add 73/81 and -73/81, the result is zero:
73/81 + (-73/81) = 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: 73/81
- Additive inverse: -73/81
To verify: 73/81 + (-73/81) = 0
Extended Mathematical Exploration of 73/81
Let's explore various mathematical operations and concepts related to 73/81 and its additive inverse -73/81.
Basic Operations and Properties
- Square of 73/81: 0.81222374638012
- Cube of 73/81: 0.73200411710801
- Square root of |73/81|: 0.94933374947973
- Reciprocal of 73/81: 1.1095890410959
- Double of 73/81: 1.8024691358025
- Half of 73/81: 0.45061728395062
- Absolute value of 73/81: 0.90123456790123
Trigonometric Functions
- Sine of 73/81: 0.78409373218958
- Cosine of 73/81: 0.62064242454171
- Tangent of 73/81: 1.2633582578061
Exponential and Logarithmic Functions
- e^73/81: 2.4626415333911
- Natural log of 73/81: -0.10398971352405
Floor and Ceiling Functions
- Floor of 73/81: 0
- Ceiling of 73/81: 1
Interesting Properties and Relationships
- The sum of 73/81 and its additive inverse (-73/81) is always 0.
- The product of 73/81 and its additive inverse is: -5329
- The average of 73/81 and its additive inverse is always 0.
- The distance between 73/81 and its additive inverse on a number line is: 146
Applications in Algebra
Consider the equation: x + 73/81 = 0
The solution to this equation is x = -73/81, which is the additive inverse of 73/81.
Graphical Representation
On a coordinate plane:
- The point (73/81, 0) is reflected across the y-axis to (-73/81, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 73/81 and Its Additive Inverse
Consider the alternating series: 73/81 + (-73/81) + 73/81 + (-73/81) + ...
The sum of this series oscillates between 0 and 73/81, never converging unless 73/81 is 0.
In Number Theory
For integer values:
- If 73/81 is even, its additive inverse is also even.
- If 73/81 is odd, its additive inverse is also odd.
- The sum of the digits of 73/81 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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