89/90 Additive Inverse :
The additive inverse of 89/90 is -89/90.
This means that when we add 89/90 and -89/90, the result is zero:
89/90 + (-89/90) = 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: 89/90
- Additive inverse: -89/90
To verify: 89/90 + (-89/90) = 0
Extended Mathematical Exploration of 89/90
Let's explore various mathematical operations and concepts related to 89/90 and its additive inverse -89/90.
Basic Operations and Properties
- Square of 89/90: 0.9779012345679
- Cube of 89/90: 0.96703566529492
- Square root of |89/90|: 0.99442892601175
- Reciprocal of 89/90: 1.0112359550562
- Double of 89/90: 1.9777777777778
- Half of 89/90: 0.49444444444444
- Absolute value of 89/90: 0.98888888888889
Trigonometric Functions
- Sine of 89/90: 0.83541580725995
- Cosine of 89/90: 0.54961843944704
- Tangent of 89/90: 1.5199923206733
Exponential and Logarithmic Functions
- e^89/90: 2.6882458724652
- Natural log of 89/90: -0.011173300598125
Floor and Ceiling Functions
- Floor of 89/90: 0
- Ceiling of 89/90: 1
Interesting Properties and Relationships
- The sum of 89/90 and its additive inverse (-89/90) is always 0.
- The product of 89/90 and its additive inverse is: -7921
- The average of 89/90 and its additive inverse is always 0.
- The distance between 89/90 and its additive inverse on a number line is: 178
Applications in Algebra
Consider the equation: x + 89/90 = 0
The solution to this equation is x = -89/90, which is the additive inverse of 89/90.
Graphical Representation
On a coordinate plane:
- The point (89/90, 0) is reflected across the y-axis to (-89/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 89/90 and Its Additive Inverse
Consider the alternating series: 89/90 + (-89/90) + 89/90 + (-89/90) + ...
The sum of this series oscillates between 0 and 89/90, never converging unless 89/90 is 0.
In Number Theory
For integer values:
- If 89/90 is even, its additive inverse is also even.
- If 89/90 is odd, its additive inverse is also odd.
- The sum of the digits of 89/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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