1/13 Additive Inverse :
The additive inverse of 1/13 is -1/13.
This means that when we add 1/13 and -1/13, the result is zero:
1/13 + (-1/13) = 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: 1/13
- Additive inverse: -1/13
To verify: 1/13 + (-1/13) = 0
Extended Mathematical Exploration of 1/13
Let's explore various mathematical operations and concepts related to 1/13 and its additive inverse -1/13.
Basic Operations and Properties
- Square of 1/13: 0.0059171597633136
- Cube of 1/13: 0.00045516613563951
- Square root of |1/13|: 0.27735009811261
- Reciprocal of 1/13: 13
- Double of 1/13: 0.15384615384615
- Half of 1/13: 0.038461538461538
- Absolute value of 1/13: 0.076923076923077
Trigonometric Functions
- Sine of 1/13: 0.076847238341398
- Cosine of 1/13: 0.99704287869645
- Tangent of 1/13: 0.077075158935862
Exponential and Logarithmic Functions
- e^1/13: 1.0799589994282
- Natural log of 1/13: -2.5649493574615
Floor and Ceiling Functions
- Floor of 1/13: 0
- Ceiling of 1/13: 1
Interesting Properties and Relationships
- The sum of 1/13 and its additive inverse (-1/13) is always 0.
- The product of 1/13 and its additive inverse is: -1
- The average of 1/13 and its additive inverse is always 0.
- The distance between 1/13 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/13 = 0
The solution to this equation is x = -1/13, which is the additive inverse of 1/13.
Graphical Representation
On a coordinate plane:
- The point (1/13, 0) is reflected across the y-axis to (-1/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/13 and Its Additive Inverse
Consider the alternating series: 1/13 + (-1/13) + 1/13 + (-1/13) + ...
The sum of this series oscillates between 0 and 1/13, never converging unless 1/13 is 0.
In Number Theory
For integer values:
- If 1/13 is even, its additive inverse is also even.
- If 1/13 is odd, its additive inverse is also odd.
- The sum of the digits of 1/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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