13/22 Additive Inverse :
The additive inverse of 13/22 is -13/22.
This means that when we add 13/22 and -13/22, the result is zero:
13/22 + (-13/22) = 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: 13/22
- Additive inverse: -13/22
To verify: 13/22 + (-13/22) = 0
Extended Mathematical Exploration of 13/22
Let's explore various mathematical operations and concepts related to 13/22 and its additive inverse -13/22.
Basic Operations and Properties
- Square of 13/22: 0.34917355371901
- Cube of 13/22: 0.2063298271976
- Square root of |13/22|: 0.76870611478581
- Reciprocal of 13/22: 1.6923076923077
- Double of 13/22: 1.1818181818182
- Half of 13/22: 0.29545454545455
- Absolute value of 13/22: 0.59090909090909
Trigonometric Functions
- Sine of 13/22: 0.55711619352486
- Cosine of 13/22: 0.83043455305783
- Tangent of 13/22: 0.6708730886419
Exponential and Logarithmic Functions
- e^13/22: 1.8056291505421
- Natural log of 13/22: -0.52609309589678
Floor and Ceiling Functions
- Floor of 13/22: 0
- Ceiling of 13/22: 1
Interesting Properties and Relationships
- The sum of 13/22 and its additive inverse (-13/22) is always 0.
- The product of 13/22 and its additive inverse is: -169
- The average of 13/22 and its additive inverse is always 0.
- The distance between 13/22 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13/22 = 0
The solution to this equation is x = -13/22, which is the additive inverse of 13/22.
Graphical Representation
On a coordinate plane:
- The point (13/22, 0) is reflected across the y-axis to (-13/22, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13/22 and Its Additive Inverse
Consider the alternating series: 13/22 + (-13/22) + 13/22 + (-13/22) + ...
The sum of this series oscillates between 0 and 13/22, never converging unless 13/22 is 0.
In Number Theory
For integer values:
- If 13/22 is even, its additive inverse is also even.
- If 13/22 is odd, its additive inverse is also odd.
- The sum of the digits of 13/22 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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