8/13 Additive Inverse :
The additive inverse of 8/13 is -8/13.
This means that when we add 8/13 and -8/13, the result is zero:
8/13 + (-8/13) = 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: 8/13
- Additive inverse: -8/13
To verify: 8/13 + (-8/13) = 0
Extended Mathematical Exploration of 8/13
Let's explore various mathematical operations and concepts related to 8/13 and its additive inverse -8/13.
Basic Operations and Properties
- Square of 8/13: 0.37869822485207
- Cube of 8/13: 0.23304506144743
- Square root of |8/13|: 0.78446454055274
- Reciprocal of 8/13: 1.625
- Double of 8/13: 1.2307692307692
- Half of 8/13: 0.30769230769231
- Absolute value of 8/13: 0.61538461538462
Trigonometric Functions
- Sine of 8/13: 0.57727262323663
- Cosine of 8/13: 0.8165514793701
- Tangent of 8/13: 0.70696415084808
Exponential and Logarithmic Functions
- e^8/13: 1.8503681427692
- Natural log of 8/13: -0.4855078157817
Floor and Ceiling Functions
- Floor of 8/13: 0
- Ceiling of 8/13: 1
Interesting Properties and Relationships
- The sum of 8/13 and its additive inverse (-8/13) is always 0.
- The product of 8/13 and its additive inverse is: -64
- The average of 8/13 and its additive inverse is always 0.
- The distance between 8/13 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8/13 = 0
The solution to this equation is x = -8/13, which is the additive inverse of 8/13.
Graphical Representation
On a coordinate plane:
- The point (8/13, 0) is reflected across the y-axis to (-8/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8/13 and Its Additive Inverse
Consider the alternating series: 8/13 + (-8/13) + 8/13 + (-8/13) + ...
The sum of this series oscillates between 0 and 8/13, never converging unless 8/13 is 0.
In Number Theory
For integer values:
- If 8/13 is even, its additive inverse is also even.
- If 8/13 is odd, its additive inverse is also odd.
- The sum of the digits of 8/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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