6/13 Additive Inverse :
The additive inverse of 6/13 is -6/13.
This means that when we add 6/13 and -6/13, the result is zero:
6/13 + (-6/13) = 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: 6/13
- Additive inverse: -6/13
To verify: 6/13 + (-6/13) = 0
Extended Mathematical Exploration of 6/13
Let's explore various mathematical operations and concepts related to 6/13 and its additive inverse -6/13.
Basic Operations and Properties
- Square of 6/13: 0.21301775147929
- Cube of 6/13: 0.098315885298134
- Square root of |6/13|: 0.67936622048676
- Reciprocal of 6/13: 2.1666666666667
- Double of 6/13: 0.92307692307692
- Half of 6/13: 0.23076923076923
- Absolute value of 6/13: 0.46153846153846
Trigonometric Functions
- Sine of 6/13: 0.44532612334333
- Cosine of 6/13: 0.89536844029037
- Tangent of 6/13: 0.49736633915633
Exponential and Logarithmic Functions
- e^6/13: 1.5865128975
- Natural log of 6/13: -0.77318988823348
Floor and Ceiling Functions
- Floor of 6/13: 0
- Ceiling of 6/13: 1
Interesting Properties and Relationships
- The sum of 6/13 and its additive inverse (-6/13) is always 0.
- The product of 6/13 and its additive inverse is: -36
- The average of 6/13 and its additive inverse is always 0.
- The distance between 6/13 and its additive inverse on a number line is: 12
Applications in Algebra
Consider the equation: x + 6/13 = 0
The solution to this equation is x = -6/13, which is the additive inverse of 6/13.
Graphical Representation
On a coordinate plane:
- The point (6/13, 0) is reflected across the y-axis to (-6/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 6/13 and Its Additive Inverse
Consider the alternating series: 6/13 + (-6/13) + 6/13 + (-6/13) + ...
The sum of this series oscillates between 0 and 6/13, never converging unless 6/13 is 0.
In Number Theory
For integer values:
- If 6/13 is even, its additive inverse is also even.
- If 6/13 is odd, its additive inverse is also odd.
- The sum of the digits of 6/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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