14/17 Additive Inverse :
The additive inverse of 14/17 is -14/17.
This means that when we add 14/17 and -14/17, the result is zero:
14/17 + (-14/17) = 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: 14/17
- Additive inverse: -14/17
To verify: 14/17 + (-14/17) = 0
Extended Mathematical Exploration of 14/17
Let's explore various mathematical operations and concepts related to 14/17 and its additive inverse -14/17.
Basic Operations and Properties
- Square of 14/17: 0.67820069204152
- Cube of 14/17: 0.55851821697537
- Square root of |14/17|: 0.90748521297303
- Reciprocal of 14/17: 1.2142857142857
- Double of 14/17: 1.6470588235294
- Half of 14/17: 0.41176470588235
- Absolute value of 14/17: 0.82352941176471
Trigonometric Functions
- Sine of 14/17: 0.73354911043833
- Cosine of 14/17: 0.67963644882771
- Tangent of 14/17: 1.0793257361397
Exponential and Logarithmic Functions
- e^14/17: 2.278527524544
- Natural log of 14/17: -0.19415601444096
Floor and Ceiling Functions
- Floor of 14/17: 0
- Ceiling of 14/17: 1
Interesting Properties and Relationships
- The sum of 14/17 and its additive inverse (-14/17) is always 0.
- The product of 14/17 and its additive inverse is: -196
- The average of 14/17 and its additive inverse is always 0.
- The distance between 14/17 and its additive inverse on a number line is: 28
Applications in Algebra
Consider the equation: x + 14/17 = 0
The solution to this equation is x = -14/17, which is the additive inverse of 14/17.
Graphical Representation
On a coordinate plane:
- The point (14/17, 0) is reflected across the y-axis to (-14/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 14/17 and Its Additive Inverse
Consider the alternating series: 14/17 + (-14/17) + 14/17 + (-14/17) + ...
The sum of this series oscillates between 0 and 14/17, never converging unless 14/17 is 0.
In Number Theory
For integer values:
- If 14/17 is even, its additive inverse is also even.
- If 14/17 is odd, its additive inverse is also odd.
- The sum of the digits of 14/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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