20/21 Additive Inverse :
The additive inverse of 20/21 is -20/21.
This means that when we add 20/21 and -20/21, the result is zero:
20/21 + (-20/21) = 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: 20/21
- Additive inverse: -20/21
To verify: 20/21 + (-20/21) = 0
Extended Mathematical Exploration of 20/21
Let's explore various mathematical operations and concepts related to 20/21 and its additive inverse -20/21.
Basic Operations and Properties
- Square of 20/21: 0.90702947845805
- Cube of 20/21: 0.86383759853148
- Square root of |20/21|: 0.97590007294853
- Reciprocal of 20/21: 1.05
- Double of 20/21: 1.9047619047619
- Half of 20/21: 0.47619047619048
- Absolute value of 20/21: 0.95238095238095
Trigonometric Functions
- Sine of 20/21: 0.81479815761924
- Cosine of 20/21: 0.57974473895008
- Tangent of 20/21: 1.4054429525222
Exponential and Logarithmic Functions
- e^20/21: 2.5918734458149
- Natural log of 20/21: -0.048790164169432
Floor and Ceiling Functions
- Floor of 20/21: 0
- Ceiling of 20/21: 1
Interesting Properties and Relationships
- The sum of 20/21 and its additive inverse (-20/21) is always 0.
- The product of 20/21 and its additive inverse is: -400
- The average of 20/21 and its additive inverse is always 0.
- The distance between 20/21 and its additive inverse on a number line is: 40
Applications in Algebra
Consider the equation: x + 20/21 = 0
The solution to this equation is x = -20/21, which is the additive inverse of 20/21.
Graphical Representation
On a coordinate plane:
- The point (20/21, 0) is reflected across the y-axis to (-20/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 20/21 and Its Additive Inverse
Consider the alternating series: 20/21 + (-20/21) + 20/21 + (-20/21) + ...
The sum of this series oscillates between 0 and 20/21, never converging unless 20/21 is 0.
In Number Theory
For integer values:
- If 20/21 is even, its additive inverse is also even.
- If 20/21 is odd, its additive inverse is also odd.
- The sum of the digits of 20/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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