5/13 Additive Inverse :
The additive inverse of 5/13 is -5/13.
This means that when we add 5/13 and -5/13, the result is zero:
5/13 + (-5/13) = 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: 5/13
- Additive inverse: -5/13
To verify: 5/13 + (-5/13) = 0
Extended Mathematical Exploration of 5/13
Let's explore various mathematical operations and concepts related to 5/13 and its additive inverse -5/13.
Basic Operations and Properties
- Square of 5/13: 0.14792899408284
- Cube of 5/13: 0.056895766954939
- Square root of |5/13|: 0.62017367294604
- Reciprocal of 5/13: 2.6
- Double of 5/13: 0.76923076923077
- Half of 5/13: 0.19230769230769
- Absolute value of 5/13: 0.38461538461538
Trigonometric Functions
- Sine of 5/13: 0.3752026480426
- Cosine of 5/13: 0.92694280994127
- Tangent of 5/13: 0.40477432266439
Exponential and Logarithmic Functions
- e^5/13: 1.469049193849
- Natural log of 5/13: -0.95551144502744
Floor and Ceiling Functions
- Floor of 5/13: 0
- Ceiling of 5/13: 1
Interesting Properties and Relationships
- The sum of 5/13 and its additive inverse (-5/13) is always 0.
- The product of 5/13 and its additive inverse is: -25
- The average of 5/13 and its additive inverse is always 0.
- The distance between 5/13 and its additive inverse on a number line is: 10
Applications in Algebra
Consider the equation: x + 5/13 = 0
The solution to this equation is x = -5/13, which is the additive inverse of 5/13.
Graphical Representation
On a coordinate plane:
- The point (5/13, 0) is reflected across the y-axis to (-5/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 5/13 and Its Additive Inverse
Consider the alternating series: 5/13 + (-5/13) + 5/13 + (-5/13) + ...
The sum of this series oscillates between 0 and 5/13, never converging unless 5/13 is 0.
In Number Theory
For integer values:
- If 5/13 is even, its additive inverse is also even.
- If 5/13 is odd, its additive inverse is also odd.
- The sum of the digits of 5/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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