1/11 Additive Inverse :
The additive inverse of 1/11 is -1/11.
This means that when we add 1/11 and -1/11, the result is zero:
1/11 + (-1/11) = 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: 1/11
- Additive inverse: -1/11
To verify: 1/11 + (-1/11) = 0
Extended Mathematical Exploration of 1/11
Let's explore various mathematical operations and concepts related to 1/11 and its additive inverse -1/11.
Basic Operations and Properties
- Square of 1/11: 0.0082644628099174
- Cube of 1/11: 0.00075131480090158
- Square root of |1/11|: 0.30151134457776
- Reciprocal of 1/11: 11
- Double of 1/11: 0.18181818181818
- Half of 1/11: 0.045454545454545
- Absolute value of 1/11: 0.090909090909091
Trigonometric Functions
- Sine of 1/11: 0.09078392350887
- Cosine of 1/11: 0.99587061370056
- Tangent of 1/11: 0.091160359849886
Exponential and Logarithmic Functions
- e^1/11: 1.0951694398747
- Natural log of 1/11: -2.3978952727984
Floor and Ceiling Functions
- Floor of 1/11: 0
- Ceiling of 1/11: 1
Interesting Properties and Relationships
- The sum of 1/11 and its additive inverse (-1/11) is always 0.
- The product of 1/11 and its additive inverse is: -1
- The average of 1/11 and its additive inverse is always 0.
- The distance between 1/11 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/11 = 0
The solution to this equation is x = -1/11, which is the additive inverse of 1/11.
Graphical Representation
On a coordinate plane:
- The point (1/11, 0) is reflected across the y-axis to (-1/11, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/11 and Its Additive Inverse
Consider the alternating series: 1/11 + (-1/11) + 1/11 + (-1/11) + ...
The sum of this series oscillates between 0 and 1/11, never converging unless 1/11 is 0.
In Number Theory
For integer values:
- If 1/11 is even, its additive inverse is also even.
- If 1/11 is odd, its additive inverse is also odd.
- The sum of the digits of 1/11 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: