16/17 Additive Inverse :
The additive inverse of 16/17 is -16/17.
This means that when we add 16/17 and -16/17, the result is zero:
16/17 + (-16/17) = 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: 16/17
- Additive inverse: -16/17
To verify: 16/17 + (-16/17) = 0
Extended Mathematical Exploration of 16/17
Let's explore various mathematical operations and concepts related to 16/17 and its additive inverse -16/17.
Basic Operations and Properties
- Square of 16/17: 0.88581314878893
- Cube of 16/17: 0.83370649297781
- Square root of |16/17|: 0.97014250014533
- Reciprocal of 16/17: 1.0625
- Double of 16/17: 1.8823529411765
- Half of 16/17: 0.47058823529412
- Absolute value of 16/17: 0.94117647058824
Trigonometric Functions
- Sine of 16/17: 0.80825140964612
- Cosine of 16/17: 0.58883754873909
- Tangent of 16/17: 1.372622060833
Exponential and Logarithmic Functions
- e^16/17: 2.5629949334828
- Natural log of 16/17: -0.060624621816435
Floor and Ceiling Functions
- Floor of 16/17: 0
- Ceiling of 16/17: 1
Interesting Properties and Relationships
- The sum of 16/17 and its additive inverse (-16/17) is always 0.
- The product of 16/17 and its additive inverse is: -256
- The average of 16/17 and its additive inverse is always 0.
- The distance between 16/17 and its additive inverse on a number line is: 32
Applications in Algebra
Consider the equation: x + 16/17 = 0
The solution to this equation is x = -16/17, which is the additive inverse of 16/17.
Graphical Representation
On a coordinate plane:
- The point (16/17, 0) is reflected across the y-axis to (-16/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 16/17 and Its Additive Inverse
Consider the alternating series: 16/17 + (-16/17) + 16/17 + (-16/17) + ...
The sum of this series oscillates between 0 and 16/17, never converging unless 16/17 is 0.
In Number Theory
For integer values:
- If 16/17 is even, its additive inverse is also even.
- If 16/17 is odd, its additive inverse is also odd.
- The sum of the digits of 16/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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