11/17 Additive Inverse :
The additive inverse of 11/17 is -11/17.
This means that when we add 11/17 and -11/17, the result is zero:
11/17 + (-11/17) = 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: 11/17
- Additive inverse: -11/17
To verify: 11/17 + (-11/17) = 0
Extended Mathematical Exploration of 11/17
Let's explore various mathematical operations and concepts related to 11/17 and its additive inverse -11/17.
Basic Operations and Properties
- Square of 11/17: 0.41868512110727
- Cube of 11/17: 0.27091390189294
- Square root of |11/17|: 0.80439966653984
- Reciprocal of 11/17: 1.5454545454545
- Double of 11/17: 1.2941176470588
- Half of 11/17: 0.32352941176471
- Absolute value of 11/17: 0.64705882352941
Trigonometric Functions
- Sine of 11/17: 0.60284236858851
- Cosine of 11/17: 0.79786031273312
- Tangent of 11/17: 0.75557382535225
Exponential and Logarithmic Functions
- e^11/17: 1.9099151624936
- Natural log of 11/17: -0.43531807125785
Floor and Ceiling Functions
- Floor of 11/17: 0
- Ceiling of 11/17: 1
Interesting Properties and Relationships
- The sum of 11/17 and its additive inverse (-11/17) is always 0.
- The product of 11/17 and its additive inverse is: -121
- The average of 11/17 and its additive inverse is always 0.
- The distance between 11/17 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/17 = 0
The solution to this equation is x = -11/17, which is the additive inverse of 11/17.
Graphical Representation
On a coordinate plane:
- The point (11/17, 0) is reflected across the y-axis to (-11/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/17 and Its Additive Inverse
Consider the alternating series: 11/17 + (-11/17) + 11/17 + (-11/17) + ...
The sum of this series oscillates between 0 and 11/17, never converging unless 11/17 is 0.
In Number Theory
For integer values:
- If 11/17 is even, its additive inverse is also even.
- If 11/17 is odd, its additive inverse is also odd.
- The sum of the digits of 11/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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