13/23 Additive Inverse :
The additive inverse of 13/23 is -13/23.
This means that when we add 13/23 and -13/23, the result is zero:
13/23 + (-13/23) = 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: 13/23
- Additive inverse: -13/23
To verify: 13/23 + (-13/23) = 0
Extended Mathematical Exploration of 13/23
Let's explore various mathematical operations and concepts related to 13/23 and its additive inverse -13/23.
Basic Operations and Properties
- Square of 13/23: 0.31947069943289
- Cube of 13/23: 0.18057039533163
- Square root of |13/23|: 0.75180941155611
- Reciprocal of 13/23: 1.7692307692308
- Double of 13/23: 1.1304347826087
- Half of 13/23: 0.28260869565217
- Absolute value of 13/23: 0.56521739130435
Trigonometric Functions
- Sine of 13/23: 0.53559940957562
- Cosine of 13/23: 0.84447218572446
- Tangent of 13/23: 0.63424162290927
Exponential and Logarithmic Functions
- e^13/23: 1.7598303129481
- Natural log of 13/23: -0.57054485846761
Floor and Ceiling Functions
- Floor of 13/23: 0
- Ceiling of 13/23: 1
Interesting Properties and Relationships
- The sum of 13/23 and its additive inverse (-13/23) is always 0.
- The product of 13/23 and its additive inverse is: -169
- The average of 13/23 and its additive inverse is always 0.
- The distance between 13/23 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13/23 = 0
The solution to this equation is x = -13/23, which is the additive inverse of 13/23.
Graphical Representation
On a coordinate plane:
- The point (13/23, 0) is reflected across the y-axis to (-13/23, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13/23 and Its Additive Inverse
Consider the alternating series: 13/23 + (-13/23) + 13/23 + (-13/23) + ...
The sum of this series oscillates between 0 and 13/23, never converging unless 13/23 is 0.
In Number Theory
For integer values:
- If 13/23 is even, its additive inverse is also even.
- If 13/23 is odd, its additive inverse is also odd.
- The sum of the digits of 13/23 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: