81/90 Additive Inverse :
The additive inverse of 81/90 is -81/90.
This means that when we add 81/90 and -81/90, the result is zero:
81/90 + (-81/90) = 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: 81/90
- Additive inverse: -81/90
To verify: 81/90 + (-81/90) = 0
Extended Mathematical Exploration of 81/90
Let's explore various mathematical operations and concepts related to 81/90 and its additive inverse -81/90.
Basic Operations and Properties
- Square of 81/90: 0.81
- Cube of 81/90: 0.729
- Square root of |81/90|: 0.94868329805051
- Reciprocal of 81/90: 1.1111111111111
- Double of 81/90: 1.8
- Half of 81/90: 0.45
- Absolute value of 81/90: 0.9
Trigonometric Functions
- Sine of 81/90: 0.78332690962748
- Cosine of 81/90: 0.62160996827066
- Tangent of 81/90: 1.2601582175503
Exponential and Logarithmic Functions
- e^81/90: 2.4596031111569
- Natural log of 81/90: -0.10536051565783
Floor and Ceiling Functions
- Floor of 81/90: 0
- Ceiling of 81/90: 1
Interesting Properties and Relationships
- The sum of 81/90 and its additive inverse (-81/90) is always 0.
- The product of 81/90 and its additive inverse is: -6561
- The average of 81/90 and its additive inverse is always 0.
- The distance between 81/90 and its additive inverse on a number line is: 162
Applications in Algebra
Consider the equation: x + 81/90 = 0
The solution to this equation is x = -81/90, which is the additive inverse of 81/90.
Graphical Representation
On a coordinate plane:
- The point (81/90, 0) is reflected across the y-axis to (-81/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 81/90 and Its Additive Inverse
Consider the alternating series: 81/90 + (-81/90) + 81/90 + (-81/90) + ...
The sum of this series oscillates between 0 and 81/90, never converging unless 81/90 is 0.
In Number Theory
For integer values:
- If 81/90 is even, its additive inverse is also even.
- If 81/90 is odd, its additive inverse is also odd.
- The sum of the digits of 81/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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