8/17 Additive Inverse :
The additive inverse of 8/17 is -8/17.
This means that when we add 8/17 and -8/17, the result is zero:
8/17 + (-8/17) = 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: 8/17
- Additive inverse: -8/17
To verify: 8/17 + (-8/17) = 0
Extended Mathematical Exploration of 8/17
Let's explore various mathematical operations and concepts related to 8/17 and its additive inverse -8/17.
Basic Operations and Properties
- Square of 8/17: 0.22145328719723
- Cube of 8/17: 0.10421331162223
- Square root of |8/17|: 0.68599434057004
- Reciprocal of 8/17: 2.125
- Double of 8/17: 0.94117647058824
- Half of 8/17: 0.23529411764706
- Absolute value of 8/17: 0.47058823529412
Trigonometric Functions
- Sine of 8/17: 0.45341065892903
- Cosine of 8/17: 0.89130173026285
- Tangent of 8/17: 0.50870613568238
Exponential and Logarithmic Functions
- e^8/17: 1.6009356431421
- Natural log of 8/17: -0.75377180237638
Floor and Ceiling Functions
- Floor of 8/17: 0
- Ceiling of 8/17: 1
Interesting Properties and Relationships
- The sum of 8/17 and its additive inverse (-8/17) is always 0.
- The product of 8/17 and its additive inverse is: -64
- The average of 8/17 and its additive inverse is always 0.
- The distance between 8/17 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8/17 = 0
The solution to this equation is x = -8/17, which is the additive inverse of 8/17.
Graphical Representation
On a coordinate plane:
- The point (8/17, 0) is reflected across the y-axis to (-8/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8/17 and Its Additive Inverse
Consider the alternating series: 8/17 + (-8/17) + 8/17 + (-8/17) + ...
The sum of this series oscillates between 0 and 8/17, never converging unless 8/17 is 0.
In Number Theory
For integer values:
- If 8/17 is even, its additive inverse is also even.
- If 8/17 is odd, its additive inverse is also odd.
- The sum of the digits of 8/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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