5/11 Additive Inverse :
The additive inverse of 5/11 is -5/11.
This means that when we add 5/11 and -5/11, the result is zero:
5/11 + (-5/11) = 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: 5/11
- Additive inverse: -5/11
To verify: 5/11 + (-5/11) = 0
Extended Mathematical Exploration of 5/11
Let's explore various mathematical operations and concepts related to 5/11 and its additive inverse -5/11.
Basic Operations and Properties
- Square of 5/11: 0.20661157024793
- Cube of 5/11: 0.093914350112697
- Square root of |5/11|: 0.67419986246324
- Reciprocal of 5/11: 2.2
- Double of 5/11: 0.90909090909091
- Half of 5/11: 0.22727272727273
- Absolute value of 5/11: 0.45454545454545
Trigonometric Functions
- Sine of 5/11: 0.43905396795356
- Cosine of 5/11: 0.89846069097331
- Tangent of 5/11: 0.48867354171937
Exponential and Logarithmic Functions
- e^5/11: 1.5754571033903
- Natural log of 5/11: -0.78845736036427
Floor and Ceiling Functions
- Floor of 5/11: 0
- Ceiling of 5/11: 1
Interesting Properties and Relationships
- The sum of 5/11 and its additive inverse (-5/11) is always 0.
- The product of 5/11 and its additive inverse is: -25
- The average of 5/11 and its additive inverse is always 0.
- The distance between 5/11 and its additive inverse on a number line is: 10
Applications in Algebra
Consider the equation: x + 5/11 = 0
The solution to this equation is x = -5/11, which is the additive inverse of 5/11.
Graphical Representation
On a coordinate plane:
- The point (5/11, 0) is reflected across the y-axis to (-5/11, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 5/11 and Its Additive Inverse
Consider the alternating series: 5/11 + (-5/11) + 5/11 + (-5/11) + ...
The sum of this series oscillates between 0 and 5/11, never converging unless 5/11 is 0.
In Number Theory
For integer values:
- If 5/11 is even, its additive inverse is also even.
- If 5/11 is odd, its additive inverse is also odd.
- The sum of the digits of 5/11 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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