17/31 Additive Inverse :
The additive inverse of 17/31 is -17/31.
This means that when we add 17/31 and -17/31, the result is zero:
17/31 + (-17/31) = 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: 17/31
- Additive inverse: -17/31
To verify: 17/31 + (-17/31) = 0
Extended Mathematical Exploration of 17/31
Let's explore various mathematical operations and concepts related to 17/31 and its additive inverse -17/31.
Basic Operations and Properties
- Square of 17/31: 0.30072840790843
- Cube of 17/31: 0.16491557853043
- Square root of |17/31|: 0.74053163117735
- Reciprocal of 17/31: 1.8235294117647
- Double of 17/31: 1.0967741935484
- Half of 17/31: 0.2741935483871
- Absolute value of 17/31: 0.54838709677419
Trigonometric Functions
- Sine of 17/31: 0.52131151010115
- Cosine of 17/31: 0.85336645670899
- Tangent of 17/31: 0.61088821338443
Exponential and Logarithmic Functions
- e^17/31: 1.7304597017636
- Natural log of 17/31: -0.60077386042893
Floor and Ceiling Functions
- Floor of 17/31: 0
- Ceiling of 17/31: 1
Interesting Properties and Relationships
- The sum of 17/31 and its additive inverse (-17/31) is always 0.
- The product of 17/31 and its additive inverse is: -289
- The average of 17/31 and its additive inverse is always 0.
- The distance between 17/31 and its additive inverse on a number line is: 34
Applications in Algebra
Consider the equation: x + 17/31 = 0
The solution to this equation is x = -17/31, which is the additive inverse of 17/31.
Graphical Representation
On a coordinate plane:
- The point (17/31, 0) is reflected across the y-axis to (-17/31, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 17/31 and Its Additive Inverse
Consider the alternating series: 17/31 + (-17/31) + 17/31 + (-17/31) + ...
The sum of this series oscillates between 0 and 17/31, never converging unless 17/31 is 0.
In Number Theory
For integer values:
- If 17/31 is even, its additive inverse is also even.
- If 17/31 is odd, its additive inverse is also odd.
- The sum of the digits of 17/31 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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