10/13 Additive Inverse :
The additive inverse of 10/13 is -10/13.
This means that when we add 10/13 and -10/13, the result is zero:
10/13 + (-10/13) = 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: 10/13
- Additive inverse: -10/13
To verify: 10/13 + (-10/13) = 0
Extended Mathematical Exploration of 10/13
Let's explore various mathematical operations and concepts related to 10/13 and its additive inverse -10/13.
Basic Operations and Properties
- Square of 10/13: 0.59171597633136
- Cube of 10/13: 0.45516613563951
- Square root of |10/13|: 0.87705801930703
- Reciprocal of 10/13: 1.3
- Double of 10/13: 1.5384615384615
- Half of 10/13: 0.38461538461538
- Absolute value of 10/13: 0.76923076923077
Trigonometric Functions
- Sine of 10/13: 0.69558279374803
- Cosine of 10/13: 0.71844594580364
- Tangent of 10/13: 0.96817693496756
Exponential and Logarithmic Functions
- e^10/13: 2.1581055339484
- Natural log of 10/13: -0.26236426446749
Floor and Ceiling Functions
- Floor of 10/13: 0
- Ceiling of 10/13: 1
Interesting Properties and Relationships
- The sum of 10/13 and its additive inverse (-10/13) is always 0.
- The product of 10/13 and its additive inverse is: -100
- The average of 10/13 and its additive inverse is always 0.
- The distance between 10/13 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/13 = 0
The solution to this equation is x = -10/13, which is the additive inverse of 10/13.
Graphical Representation
On a coordinate plane:
- The point (10/13, 0) is reflected across the y-axis to (-10/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/13 and Its Additive Inverse
Consider the alternating series: 10/13 + (-10/13) + 10/13 + (-10/13) + ...
The sum of this series oscillates between 0 and 10/13, never converging unless 10/13 is 0.
In Number Theory
For integer values:
- If 10/13 is even, its additive inverse is also even.
- If 10/13 is odd, its additive inverse is also odd.
- The sum of the digits of 10/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: