90/101 Additive Inverse :
The additive inverse of 90/101 is -90/101.
This means that when we add 90/101 and -90/101, the result is zero:
90/101 + (-90/101) = 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: 90/101
- Additive inverse: -90/101
To verify: 90/101 + (-90/101) = 0
Extended Mathematical Exploration of 90/101
Let's explore various mathematical operations and concepts related to 90/101 and its additive inverse -90/101.
Basic Operations and Properties
- Square of 90/101: 0.79403980001961
- Cube of 90/101: 0.70756021783925
- Square root of |90/101|: 0.94397516329133
- Reciprocal of 90/101: 1.1222222222222
- Double of 90/101: 1.7821782178218
- Half of 90/101: 0.44554455445545
- Absolute value of 90/101: 0.89108910891089
Trigonometric Functions
- Sine of 90/101: 0.77775678477309
- Cosine of 90/101: 0.62856533768529
- Tangent of 90/101: 1.2373523294129
Exponential and Logarithmic Functions
- e^90/101: 2.4377832174412
- Natural log of 90/101: -0.11531084651099
Floor and Ceiling Functions
- Floor of 90/101: 0
- Ceiling of 90/101: 1
Interesting Properties and Relationships
- The sum of 90/101 and its additive inverse (-90/101) is always 0.
- The product of 90/101 and its additive inverse is: -8100
- The average of 90/101 and its additive inverse is always 0.
- The distance between 90/101 and its additive inverse on a number line is: 180
Applications in Algebra
Consider the equation: x + 90/101 = 0
The solution to this equation is x = -90/101, which is the additive inverse of 90/101.
Graphical Representation
On a coordinate plane:
- The point (90/101, 0) is reflected across the y-axis to (-90/101, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 90/101 and Its Additive Inverse
Consider the alternating series: 90/101 + (-90/101) + 90/101 + (-90/101) + ...
The sum of this series oscillates between 0 and 90/101, never converging unless 90/101 is 0.
In Number Theory
For integer values:
- If 90/101 is even, its additive inverse is also even.
- If 90/101 is odd, its additive inverse is also odd.
- The sum of the digits of 90/101 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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