3/13 Additive Inverse :
The additive inverse of 3/13 is -3/13.
This means that when we add 3/13 and -3/13, the result is zero:
3/13 + (-3/13) = 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: 3/13
- Additive inverse: -3/13
To verify: 3/13 + (-3/13) = 0
Extended Mathematical Exploration of 3/13
Let's explore various mathematical operations and concepts related to 3/13 and its additive inverse -3/13.
Basic Operations and Properties
- Square of 3/13: 0.053254437869822
- Cube of 3/13: 0.012289485662267
- Square root of |3/13|: 0.48038446141526
- Reciprocal of 3/13: 4.3333333333333
- Double of 3/13: 0.46153846153846
- Half of 3/13: 0.11538461538462
- Absolute value of 3/13: 0.23076923076923
Trigonometric Functions
- Sine of 3/13: 0.22872643016236
- Cosine of 3/13: 0.97349073962991
- Tangent of 3/13: 0.23495491107529
Exponential and Logarithmic Functions
- e^3/13: 1.2595685362456
- Natural log of 3/13: -1.4663370687934
Floor and Ceiling Functions
- Floor of 3/13: 0
- Ceiling of 3/13: 1
Interesting Properties and Relationships
- The sum of 3/13 and its additive inverse (-3/13) is always 0.
- The product of 3/13 and its additive inverse is: -9
- The average of 3/13 and its additive inverse is always 0.
- The distance between 3/13 and its additive inverse on a number line is: 6
Applications in Algebra
Consider the equation: x + 3/13 = 0
The solution to this equation is x = -3/13, which is the additive inverse of 3/13.
Graphical Representation
On a coordinate plane:
- The point (3/13, 0) is reflected across the y-axis to (-3/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 3/13 and Its Additive Inverse
Consider the alternating series: 3/13 + (-3/13) + 3/13 + (-3/13) + ...
The sum of this series oscillates between 0 and 3/13, never converging unless 3/13 is 0.
In Number Theory
For integer values:
- If 3/13 is even, its additive inverse is also even.
- If 3/13 is odd, its additive inverse is also odd.
- The sum of the digits of 3/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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