2/13 Additive Inverse :
The additive inverse of 2/13 is -2/13.
This means that when we add 2/13 and -2/13, the result is zero:
2/13 + (-2/13) = 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: 2/13
- Additive inverse: -2/13
To verify: 2/13 + (-2/13) = 0
Extended Mathematical Exploration of 2/13
Let's explore various mathematical operations and concepts related to 2/13 and its additive inverse -2/13.
Basic Operations and Properties
- Square of 2/13: 0.023668639053254
- Cube of 2/13: 0.0036413290851161
- Square root of |2/13|: 0.39223227027637
- Reciprocal of 2/13: 6.5
- Double of 2/13: 0.30769230769231
- Half of 2/13: 0.076923076923077
- Absolute value of 2/13: 0.15384615384615
Trigonometric Functions
- Sine of 2/13: 0.15323998347156
- Cosine of 2/13: 0.9881890039186
- Tangent of 2/13: 0.15507153273705
Exponential and Logarithmic Functions
- e^2/13: 1.1663114404459
- Natural log of 2/13: -1.8718021769016
Floor and Ceiling Functions
- Floor of 2/13: 0
- Ceiling of 2/13: 1
Interesting Properties and Relationships
- The sum of 2/13 and its additive inverse (-2/13) is always 0.
- The product of 2/13 and its additive inverse is: -4
- The average of 2/13 and its additive inverse is always 0.
- The distance between 2/13 and its additive inverse on a number line is: 4
Applications in Algebra
Consider the equation: x + 2/13 = 0
The solution to this equation is x = -2/13, which is the additive inverse of 2/13.
Graphical Representation
On a coordinate plane:
- The point (2/13, 0) is reflected across the y-axis to (-2/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 2/13 and Its Additive Inverse
Consider the alternating series: 2/13 + (-2/13) + 2/13 + (-2/13) + ...
The sum of this series oscillates between 0 and 2/13, never converging unless 2/13 is 0.
In Number Theory
For integer values:
- If 2/13 is even, its additive inverse is also even.
- If 2/13 is odd, its additive inverse is also odd.
- The sum of the digits of 2/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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