75/81 Additive Inverse :
The additive inverse of 75/81 is -75/81.
This means that when we add 75/81 and -75/81, the result is zero:
75/81 + (-75/81) = 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: 75/81
- Additive inverse: -75/81
To verify: 75/81 + (-75/81) = 0
Extended Mathematical Exploration of 75/81
Let's explore various mathematical operations and concepts related to 75/81 and its additive inverse -75/81.
Basic Operations and Properties
- Square of 75/81: 0.85733882030178
- Cube of 75/81: 0.79383224102017
- Square root of |75/81|: 0.96225044864938
- Reciprocal of 75/81: 1.08
- Double of 75/81: 1.8518518518519
- Half of 75/81: 0.46296296296296
- Absolute value of 75/81: 0.92592592592593
Trigonometric Functions
- Sine of 75/81: 0.79917767502713
- Cosine of 75/81: 0.60109487083008
- Tangent of 75/81: 1.3295366735096
Exponential and Logarithmic Functions
- e^75/81: 2.5242044049437
- Natural log of 75/81: -0.076961041136128
Floor and Ceiling Functions
- Floor of 75/81: 0
- Ceiling of 75/81: 1
Interesting Properties and Relationships
- The sum of 75/81 and its additive inverse (-75/81) is always 0.
- The product of 75/81 and its additive inverse is: -5625
- The average of 75/81 and its additive inverse is always 0.
- The distance between 75/81 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/81 = 0
The solution to this equation is x = -75/81, which is the additive inverse of 75/81.
Graphical Representation
On a coordinate plane:
- The point (75/81, 0) is reflected across the y-axis to (-75/81, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/81 and Its Additive Inverse
Consider the alternating series: 75/81 + (-75/81) + 75/81 + (-75/81) + ...
The sum of this series oscillates between 0 and 75/81, never converging unless 75/81 is 0.
In Number Theory
For integer values:
- If 75/81 is even, its additive inverse is also even.
- If 75/81 is odd, its additive inverse is also odd.
- The sum of the digits of 75/81 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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