20/31 Additive Inverse :
The additive inverse of 20/31 is -20/31.
This means that when we add 20/31 and -20/31, the result is zero:
20/31 + (-20/31) = 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: 20/31
- Additive inverse: -20/31
To verify: 20/31 + (-20/31) = 0
Extended Mathematical Exploration of 20/31
Let's explore various mathematical operations and concepts related to 20/31 and its additive inverse -20/31.
Basic Operations and Properties
- Square of 20/31: 0.4162330905307
- Cube of 20/31: 0.26853747776174
- Square root of |20/31|: 0.8032193289025
- Reciprocal of 20/31: 1.55
- Double of 20/31: 1.2903225806452
- Half of 20/31: 0.32258064516129
- Absolute value of 20/31: 0.64516129032258
Trigonometric Functions
- Sine of 20/31: 0.60132731775271
- Cosine of 20/31: 0.79900278905917
- Tangent of 20/31: 0.75259726998046
Exponential and Logarithmic Functions
- e^20/31: 1.9062944713278
- Natural log of 20/31: -0.43825493093116
Floor and Ceiling Functions
- Floor of 20/31: 0
- Ceiling of 20/31: 1
Interesting Properties and Relationships
- The sum of 20/31 and its additive inverse (-20/31) is always 0.
- The product of 20/31 and its additive inverse is: -400
- The average of 20/31 and its additive inverse is always 0.
- The distance between 20/31 and its additive inverse on a number line is: 40
Applications in Algebra
Consider the equation: x + 20/31 = 0
The solution to this equation is x = -20/31, which is the additive inverse of 20/31.
Graphical Representation
On a coordinate plane:
- The point (20/31, 0) is reflected across the y-axis to (-20/31, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 20/31 and Its Additive Inverse
Consider the alternating series: 20/31 + (-20/31) + 20/31 + (-20/31) + ...
The sum of this series oscillates between 0 and 20/31, never converging unless 20/31 is 0.
In Number Theory
For integer values:
- If 20/31 is even, its additive inverse is also even.
- If 20/31 is odd, its additive inverse is also odd.
- The sum of the digits of 20/31 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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