13/14 Additive Inverse :
The additive inverse of 13/14 is -13/14.
This means that when we add 13/14 and -13/14, the result is zero:
13/14 + (-13/14) = 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: 13/14
- Additive inverse: -13/14
To verify: 13/14 + (-13/14) = 0
Extended Mathematical Exploration of 13/14
Let's explore various mathematical operations and concepts related to 13/14 and its additive inverse -13/14.
Basic Operations and Properties
- Square of 13/14: 0.86224489795918
- Cube of 13/14: 0.80065597667638
- Square root of |13/14|: 0.96362411165943
- Reciprocal of 13/14: 1.0769230769231
- Double of 13/14: 1.8571428571429
- Half of 13/14: 0.46428571428571
- Absolute value of 13/14: 0.92857142857143
Trigonometric Functions
- Sine of 13/14: 0.80076507464875
- Cosine of 13/14: 0.59897854320733
- Tangent of 13/14: 1.3368844071791
Exponential and Logarithmic Functions
- e^13/14: 2.530891035224
- Natural log of 13/14: -0.074107972153722
Floor and Ceiling Functions
- Floor of 13/14: 0
- Ceiling of 13/14: 1
Interesting Properties and Relationships
- The sum of 13/14 and its additive inverse (-13/14) is always 0.
- The product of 13/14 and its additive inverse is: -169
- The average of 13/14 and its additive inverse is always 0.
- The distance between 13/14 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13/14 = 0
The solution to this equation is x = -13/14, which is the additive inverse of 13/14.
Graphical Representation
On a coordinate plane:
- The point (13/14, 0) is reflected across the y-axis to (-13/14, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13/14 and Its Additive Inverse
Consider the alternating series: 13/14 + (-13/14) + 13/14 + (-13/14) + ...
The sum of this series oscillates between 0 and 13/14, never converging unless 13/14 is 0.
In Number Theory
For integer values:
- If 13/14 is even, its additive inverse is also even.
- If 13/14 is odd, its additive inverse is also odd.
- The sum of the digits of 13/14 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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