3/11 Additive Inverse :
The additive inverse of 3/11 is -3/11.
This means that when we add 3/11 and -3/11, the result is zero:
3/11 + (-3/11) = 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: 3/11
- Additive inverse: -3/11
To verify: 3/11 + (-3/11) = 0
Extended Mathematical Exploration of 3/11
Let's explore various mathematical operations and concepts related to 3/11 and its additive inverse -3/11.
Basic Operations and Properties
- Square of 3/11: 0.074380165289256
- Cube of 3/11: 0.020285499624343
- Square root of |3/11|: 0.52223296786709
- Reciprocal of 3/11: 3.6666666666667
- Double of 3/11: 0.54545454545455
- Half of 3/11: 0.13636363636364
- Absolute value of 3/11: 0.27272727272727
Trigonometric Functions
- Sine of 3/11: 0.2693589075356
- Cosine of 3/11: 0.96303986362519
- Tangent of 3/11: 0.279696529406
Exponential and Logarithmic Functions
- e^3/11: 1.3135419572539
- Natural log of 3/11: -1.2992829841303
Floor and Ceiling Functions
- Floor of 3/11: 0
- Ceiling of 3/11: 1
Interesting Properties and Relationships
- The sum of 3/11 and its additive inverse (-3/11) is always 0.
- The product of 3/11 and its additive inverse is: -9
- The average of 3/11 and its additive inverse is always 0.
- The distance between 3/11 and its additive inverse on a number line is: 6
Applications in Algebra
Consider the equation: x + 3/11 = 0
The solution to this equation is x = -3/11, which is the additive inverse of 3/11.
Graphical Representation
On a coordinate plane:
- The point (3/11, 0) is reflected across the y-axis to (-3/11, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 3/11 and Its Additive Inverse
Consider the alternating series: 3/11 + (-3/11) + 3/11 + (-3/11) + ...
The sum of this series oscillates between 0 and 3/11, never converging unless 3/11 is 0.
In Number Theory
For integer values:
- If 3/11 is even, its additive inverse is also even.
- If 3/11 is odd, its additive inverse is also odd.
- The sum of the digits of 3/11 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: