83/90 Additive Inverse :
The additive inverse of 83/90 is -83/90.
This means that when we add 83/90 and -83/90, the result is zero:
83/90 + (-83/90) = 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: 83/90
- Additive inverse: -83/90
To verify: 83/90 + (-83/90) = 0
Extended Mathematical Exploration of 83/90
Let's explore various mathematical operations and concepts related to 83/90 and its additive inverse -83/90.
Basic Operations and Properties
- Square of 83/90: 0.85049382716049
- Cube of 83/90: 0.78434430727023
- Square root of |83/90|: 0.96032401939253
- Reciprocal of 83/90: 1.0843373493976
- Double of 83/90: 1.8444444444444
- Half of 83/90: 0.46111111111111
- Absolute value of 83/90: 0.92222222222222
Trigonometric Functions
- Sine of 83/90: 0.79694592149545
- Cosine of 83/90: 0.60405065864691
- Tangent of 83/90: 1.3193362346142
Exponential and Logarithmic Functions
- e^83/90: 2.5148727911736
- Natural log of 83/90: -0.080969062533667
Floor and Ceiling Functions
- Floor of 83/90: 0
- Ceiling of 83/90: 1
Interesting Properties and Relationships
- The sum of 83/90 and its additive inverse (-83/90) is always 0.
- The product of 83/90 and its additive inverse is: -6889
- The average of 83/90 and its additive inverse is always 0.
- The distance between 83/90 and its additive inverse on a number line is: 166
Applications in Algebra
Consider the equation: x + 83/90 = 0
The solution to this equation is x = -83/90, which is the additive inverse of 83/90.
Graphical Representation
On a coordinate plane:
- The point (83/90, 0) is reflected across the y-axis to (-83/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 83/90 and Its Additive Inverse
Consider the alternating series: 83/90 + (-83/90) + 83/90 + (-83/90) + ...
The sum of this series oscillates between 0 and 83/90, never converging unless 83/90 is 0.
In Number Theory
For integer values:
- If 83/90 is even, its additive inverse is also even.
- If 83/90 is odd, its additive inverse is also odd.
- The sum of the digits of 83/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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