82/90 Additive Inverse :
The additive inverse of 82/90 is -82/90.
This means that when we add 82/90 and -82/90, the result is zero:
82/90 + (-82/90) = 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: 82/90
- Additive inverse: -82/90
To verify: 82/90 + (-82/90) = 0
Extended Mathematical Exploration of 82/90
Let's explore various mathematical operations and concepts related to 82/90 and its additive inverse -82/90.
Basic Operations and Properties
- Square of 82/90: 0.83012345679012
- Cube of 82/90: 0.75633470507545
- Square root of |82/90|: 0.95452140421842
- Reciprocal of 82/90: 1.0975609756098
- Double of 82/90: 1.8222222222222
- Half of 82/90: 0.45555555555556
- Absolute value of 82/90: 0.91111111111111
Trigonometric Functions
- Sine of 82/90: 0.79018519192335
- Cosine of 82/90: 0.61286814443652
- Tangent of 82/90: 1.2893233219845
Exponential and Logarithmic Functions
- e^82/90: 2.4870844258558
- Natural log of 82/90: -0.093090423066012
Floor and Ceiling Functions
- Floor of 82/90: 0
- Ceiling of 82/90: 1
Interesting Properties and Relationships
- The sum of 82/90 and its additive inverse (-82/90) is always 0.
- The product of 82/90 and its additive inverse is: -6724
- The average of 82/90 and its additive inverse is always 0.
- The distance between 82/90 and its additive inverse on a number line is: 164
Applications in Algebra
Consider the equation: x + 82/90 = 0
The solution to this equation is x = -82/90, which is the additive inverse of 82/90.
Graphical Representation
On a coordinate plane:
- The point (82/90, 0) is reflected across the y-axis to (-82/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 82/90 and Its Additive Inverse
Consider the alternating series: 82/90 + (-82/90) + 82/90 + (-82/90) + ...
The sum of this series oscillates between 0 and 82/90, never converging unless 82/90 is 0.
In Number Theory
For integer values:
- If 82/90 is even, its additive inverse is also even.
- If 82/90 is odd, its additive inverse is also odd.
- The sum of the digits of 82/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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