16/31 Additive Inverse :
The additive inverse of 16/31 is -16/31.
This means that when we add 16/31 and -16/31, the result is zero:
16/31 + (-16/31) = 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: 16/31
- Additive inverse: -16/31
To verify: 16/31 + (-16/31) = 0
Extended Mathematical Exploration of 16/31
Let's explore various mathematical operations and concepts related to 16/31 and its additive inverse -16/31.
Basic Operations and Properties
- Square of 16/31: 0.26638917793965
- Cube of 16/31: 0.13749118861401
- Square root of |16/31|: 0.7184212081071
- Reciprocal of 16/31: 1.9375
- Double of 16/31: 1.0322580645161
- Half of 16/31: 0.25806451612903
- Absolute value of 16/31: 0.51612903225806
Trigonometric Functions
- Sine of 16/31: 0.49351712346433
- Cosine of 16/31: 0.86973607999639
- Tangent of 16/31: 0.5674331959028
Exponential and Logarithmic Functions
- e^16/31: 1.675529160761
- Natural log of 16/31: -0.66139848224537
Floor and Ceiling Functions
- Floor of 16/31: 0
- Ceiling of 16/31: 1
Interesting Properties and Relationships
- The sum of 16/31 and its additive inverse (-16/31) is always 0.
- The product of 16/31 and its additive inverse is: -256
- The average of 16/31 and its additive inverse is always 0.
- The distance between 16/31 and its additive inverse on a number line is: 32
Applications in Algebra
Consider the equation: x + 16/31 = 0
The solution to this equation is x = -16/31, which is the additive inverse of 16/31.
Graphical Representation
On a coordinate plane:
- The point (16/31, 0) is reflected across the y-axis to (-16/31, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 16/31 and Its Additive Inverse
Consider the alternating series: 16/31 + (-16/31) + 16/31 + (-16/31) + ...
The sum of this series oscillates between 0 and 16/31, never converging unless 16/31 is 0.
In Number Theory
For integer values:
- If 16/31 is even, its additive inverse is also even.
- If 16/31 is odd, its additive inverse is also odd.
- The sum of the digits of 16/31 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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