1/14 Additive Inverse :
The additive inverse of 1/14 is -1/14.
This means that when we add 1/14 and -1/14, the result is zero:
1/14 + (-1/14) = 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: 1/14
- Additive inverse: -1/14
To verify: 1/14 + (-1/14) = 0
Extended Mathematical Exploration of 1/14
Let's explore various mathematical operations and concepts related to 1/14 and its additive inverse -1/14.
Basic Operations and Properties
- Square of 1/14: 0.0051020408163265
- Cube of 1/14: 0.00036443148688047
- Square root of |1/14|: 0.26726124191242
- Reciprocal of 1/14: 14
- Double of 1/14: 0.14285714285714
- Half of 1/14: 0.035714285714286
- Absolute value of 1/14: 0.071428571428571
Trigonometric Functions
- Sine of 1/14: 0.071367848340079
- Cosine of 1/14: 0.99745006402492
- Tangent of 1/14: 0.071550297016469
Exponential and Logarithmic Functions
- e^1/14: 1.0740414307163
- Natural log of 1/14: -2.6390573296153
Floor and Ceiling Functions
- Floor of 1/14: 0
- Ceiling of 1/14: 1
Interesting Properties and Relationships
- The sum of 1/14 and its additive inverse (-1/14) is always 0.
- The product of 1/14 and its additive inverse is: -1
- The average of 1/14 and its additive inverse is always 0.
- The distance between 1/14 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/14 = 0
The solution to this equation is x = -1/14, which is the additive inverse of 1/14.
Graphical Representation
On a coordinate plane:
- The point (1/14, 0) is reflected across the y-axis to (-1/14, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/14 and Its Additive Inverse
Consider the alternating series: 1/14 + (-1/14) + 1/14 + (-1/14) + ...
The sum of this series oscillates between 0 and 1/14, never converging unless 1/14 is 0.
In Number Theory
For integer values:
- If 1/14 is even, its additive inverse is also even.
- If 1/14 is odd, its additive inverse is also odd.
- The sum of the digits of 1/14 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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