13/21 Additive Inverse :
The additive inverse of 13/21 is -13/21.
This means that when we add 13/21 and -13/21, the result is zero:
13/21 + (-13/21) = 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: 13/21
- Additive inverse: -13/21
To verify: 13/21 + (-13/21) = 0
Extended Mathematical Exploration of 13/21
Let's explore various mathematical operations and concepts related to 13/21 and its additive inverse -13/21.
Basic Operations and Properties
- Square of 13/21: 0.38321995464853
- Cube of 13/21: 0.23723140049671
- Square root of |13/21|: 0.78679579246944
- Reciprocal of 13/21: 1.6153846153846
- Double of 13/21: 1.2380952380952
- Half of 13/21: 0.30952380952381
- Absolute value of 13/21: 0.61904761904762
Trigonometric Functions
- Sine of 13/21: 0.58025977480681
- Cosine of 13/21: 0.81443145429259
- Tangent of 13/21: 0.7124722059155
Exponential and Logarithmic Functions
- e^13/21: 1.8571584769711
- Natural log of 13/21: -0.47957308026189
Floor and Ceiling Functions
- Floor of 13/21: 0
- Ceiling of 13/21: 1
Interesting Properties and Relationships
- The sum of 13/21 and its additive inverse (-13/21) is always 0.
- The product of 13/21 and its additive inverse is: -169
- The average of 13/21 and its additive inverse is always 0.
- The distance between 13/21 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13/21 = 0
The solution to this equation is x = -13/21, which is the additive inverse of 13/21.
Graphical Representation
On a coordinate plane:
- The point (13/21, 0) is reflected across the y-axis to (-13/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13/21 and Its Additive Inverse
Consider the alternating series: 13/21 + (-13/21) + 13/21 + (-13/21) + ...
The sum of this series oscillates between 0 and 13/21, never converging unless 13/21 is 0.
In Number Theory
For integer values:
- If 13/21 is even, its additive inverse is also even.
- If 13/21 is odd, its additive inverse is also odd.
- The sum of the digits of 13/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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