11/13 Additive Inverse :
The additive inverse of 11/13 is -11/13.
This means that when we add 11/13 and -11/13, the result is zero:
11/13 + (-11/13) = 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: 11/13
- Additive inverse: -11/13
To verify: 11/13 + (-11/13) = 0
Extended Mathematical Exploration of 11/13
Let's explore various mathematical operations and concepts related to 11/13 and its additive inverse -11/13.
Basic Operations and Properties
- Square of 11/13: 0.71597633136095
- Cube of 11/13: 0.60582612653619
- Square root of |11/13|: 0.9198662110078
- Reciprocal of 11/13: 1.1818181818182
- Double of 11/13: 1.6923076923077
- Half of 11/13: 0.42307692307692
- Absolute value of 11/13: 0.84615384615385
Trigonometric Functions
- Sine of 11/13: 0.74873645788284
- Cosine of 11/13: 0.66286779725452
- Tangent of 11/13: 1.1295411558443
Exponential and Logarithmic Functions
- e^11/13: 2.3306654931034
- Natural log of 11/13: -0.16705408466317
Floor and Ceiling Functions
- Floor of 11/13: 0
- Ceiling of 11/13: 1
Interesting Properties and Relationships
- The sum of 11/13 and its additive inverse (-11/13) is always 0.
- The product of 11/13 and its additive inverse is: -121
- The average of 11/13 and its additive inverse is always 0.
- The distance between 11/13 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/13 = 0
The solution to this equation is x = -11/13, which is the additive inverse of 11/13.
Graphical Representation
On a coordinate plane:
- The point (11/13, 0) is reflected across the y-axis to (-11/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/13 and Its Additive Inverse
Consider the alternating series: 11/13 + (-11/13) + 11/13 + (-11/13) + ...
The sum of this series oscillates between 0 and 11/13, never converging unless 11/13 is 0.
In Number Theory
For integer values:
- If 11/13 is even, its additive inverse is also even.
- If 11/13 is odd, its additive inverse is also odd.
- The sum of the digits of 11/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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