4/13 Additive Inverse :
The additive inverse of 4/13 is -4/13.
This means that when we add 4/13 and -4/13, the result is zero:
4/13 + (-4/13) = 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: 4/13
- Additive inverse: -4/13
To verify: 4/13 + (-4/13) = 0
Extended Mathematical Exploration of 4/13
Let's explore various mathematical operations and concepts related to 4/13 and its additive inverse -4/13.
Basic Operations and Properties
- Square of 4/13: 0.094674556213018
- Cube of 4/13: 0.029130632680929
- Square root of |4/13|: 0.55470019622523
- Reciprocal of 4/13: 3.25
- Double of 4/13: 0.61538461538462
- Half of 4/13: 0.15384615384615
- Absolute value of 4/13: 0.30769230769231
Trigonometric Functions
- Sine of 4/13: 0.30286013325453
- Cosine of 4/13: 0.95303501493127
- Tangent of 4/13: 0.31778489615764
Exponential and Logarithmic Functions
- e^4/13: 1.3602823761151
- Natural log of 4/13: -1.1786549963416
Floor and Ceiling Functions
- Floor of 4/13: 0
- Ceiling of 4/13: 1
Interesting Properties and Relationships
- The sum of 4/13 and its additive inverse (-4/13) is always 0.
- The product of 4/13 and its additive inverse is: -16
- The average of 4/13 and its additive inverse is always 0.
- The distance between 4/13 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4/13 = 0
The solution to this equation is x = -4/13, which is the additive inverse of 4/13.
Graphical Representation
On a coordinate plane:
- The point (4/13, 0) is reflected across the y-axis to (-4/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4/13 and Its Additive Inverse
Consider the alternating series: 4/13 + (-4/13) + 4/13 + (-4/13) + ...
The sum of this series oscillates between 0 and 4/13, never converging unless 4/13 is 0.
In Number Theory
For integer values:
- If 4/13 is even, its additive inverse is also even.
- If 4/13 is odd, its additive inverse is also odd.
- The sum of the digits of 4/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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