21/31 Additive Inverse :
The additive inverse of 21/31 is -21/31.
This means that when we add 21/31 and -21/31, the result is zero:
21/31 + (-21/31) = 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: 21/31
- Additive inverse: -21/31
To verify: 21/31 + (-21/31) = 0
Extended Mathematical Exploration of 21/31
Let's explore various mathematical operations and concepts related to 21/31 and its additive inverse -21/31.
Basic Operations and Properties
- Square of 21/31: 0.45889698231009
- Cube of 21/31: 0.31086569769393
- Square root of |21/31|: 0.8230548917531
- Reciprocal of 21/31: 1.4761904761905
- Double of 21/31: 1.3548387096774
- Half of 21/31: 0.33870967741935
- Absolute value of 21/31: 0.67741935483871
Trigonometric Functions
- Sine of 21/31: 0.626784293177
- Cosine of 21/31: 0.77919281941417
- Tangent of 21/31: 0.80440203959816
Exponential and Logarithmic Functions
- e^21/31: 1.9687904213073
- Natural log of 21/31: -0.38946476676172
Floor and Ceiling Functions
- Floor of 21/31: 0
- Ceiling of 21/31: 1
Interesting Properties and Relationships
- The sum of 21/31 and its additive inverse (-21/31) is always 0.
- The product of 21/31 and its additive inverse is: -441
- The average of 21/31 and its additive inverse is always 0.
- The distance between 21/31 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/31 = 0
The solution to this equation is x = -21/31, which is the additive inverse of 21/31.
Graphical Representation
On a coordinate plane:
- The point (21/31, 0) is reflected across the y-axis to (-21/31, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/31 and Its Additive Inverse
Consider the alternating series: 21/31 + (-21/31) + 21/31 + (-21/31) + ...
The sum of this series oscillates between 0 and 21/31, never converging unless 21/31 is 0.
In Number Theory
For integer values:
- If 21/31 is even, its additive inverse is also even.
- If 21/31 is odd, its additive inverse is also odd.
- The sum of the digits of 21/31 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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