90/91 Additive Inverse :
The additive inverse of 90/91 is -90/91.
This means that when we add 90/91 and -90/91, the result is zero:
90/91 + (-90/91) = 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: 90/91
- Additive inverse: -90/91
To verify: 90/91 + (-90/91) = 0
Extended Mathematical Exploration of 90/91
Let's explore various mathematical operations and concepts related to 90/91 and its additive inverse -90/91.
Basic Operations and Properties
- Square of 90/91: 0.97814273638449
- Cube of 90/91: 0.96739391510554
- Square root of |90/91|: 0.99449031619769
- Reciprocal of 90/91: 1.0111111111111
- Double of 90/91: 1.978021978022
- Half of 90/91: 0.49450549450549
- Absolute value of 90/91: 0.98901098901099
Trigonometric Functions
- Sine of 90/91: 0.83548290951098
- Cosine of 90/91: 0.54951643097825
- Tangent of 90/91: 1.5203965930985
Exponential and Logarithmic Functions
- e^90/91: 2.688574127654
- Natural log of 90/91: -0.011049836186585
Floor and Ceiling Functions
- Floor of 90/91: 0
- Ceiling of 90/91: 1
Interesting Properties and Relationships
- The sum of 90/91 and its additive inverse (-90/91) is always 0.
- The product of 90/91 and its additive inverse is: -8100
- The average of 90/91 and its additive inverse is always 0.
- The distance between 90/91 and its additive inverse on a number line is: 180
Applications in Algebra
Consider the equation: x + 90/91 = 0
The solution to this equation is x = -90/91, which is the additive inverse of 90/91.
Graphical Representation
On a coordinate plane:
- The point (90/91, 0) is reflected across the y-axis to (-90/91, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 90/91 and Its Additive Inverse
Consider the alternating series: 90/91 + (-90/91) + 90/91 + (-90/91) + ...
The sum of this series oscillates between 0 and 90/91, never converging unless 90/91 is 0.
In Number Theory
For integer values:
- If 90/91 is even, its additive inverse is also even.
- If 90/91 is odd, its additive inverse is also odd.
- The sum of the digits of 90/91 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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