6/21 Additive Inverse :
The additive inverse of 6/21 is -6/21.
This means that when we add 6/21 and -6/21, the result is zero:
6/21 + (-6/21) = 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: 6/21
- Additive inverse: -6/21
To verify: 6/21 + (-6/21) = 0
Extended Mathematical Exploration of 6/21
Let's explore various mathematical operations and concepts related to 6/21 and its additive inverse -6/21.
Basic Operations and Properties
- Square of 6/21: 0.081632653061224
- Cube of 6/21: 0.02332361516035
- Square root of |6/21|: 0.53452248382485
- Reciprocal of 6/21: 3.5
- Double of 6/21: 0.57142857142857
- Half of 6/21: 0.14285714285714
- Absolute value of 6/21: 0.28571428571429
Trigonometric Functions
- Sine of 6/21: 0.28184285212221
- Cosine of 6/21: 0.95946058111192
- Tangent of 6/21: 0.29375136161986
Exponential and Logarithmic Functions
- e^6/21: 1.3307121974473
- Natural log of 6/21: -1.2527629684954
Floor and Ceiling Functions
- Floor of 6/21: 0
- Ceiling of 6/21: 1
Interesting Properties and Relationships
- The sum of 6/21 and its additive inverse (-6/21) is always 0.
- The product of 6/21 and its additive inverse is: -36
- The average of 6/21 and its additive inverse is always 0.
- The distance between 6/21 and its additive inverse on a number line is: 12
Applications in Algebra
Consider the equation: x + 6/21 = 0
The solution to this equation is x = -6/21, which is the additive inverse of 6/21.
Graphical Representation
On a coordinate plane:
- The point (6/21, 0) is reflected across the y-axis to (-6/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 6/21 and Its Additive Inverse
Consider the alternating series: 6/21 + (-6/21) + 6/21 + (-6/21) + ...
The sum of this series oscillates between 0 and 6/21, never converging unless 6/21 is 0.
In Number Theory
For integer values:
- If 6/21 is even, its additive inverse is also even.
- If 6/21 is odd, its additive inverse is also odd.
- The sum of the digits of 6/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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