1/15 Additive Inverse :
The additive inverse of 1/15 is -1/15.
This means that when we add 1/15 and -1/15, the result is zero:
1/15 + (-1/15) = 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: 1/15
- Additive inverse: -1/15
To verify: 1/15 + (-1/15) = 0
Extended Mathematical Exploration of 1/15
Let's explore various mathematical operations and concepts related to 1/15 and its additive inverse -1/15.
Basic Operations and Properties
- Square of 1/15: 0.0044444444444444
- Cube of 1/15: 0.0002962962962963
- Square root of |1/15|: 0.25819888974716
- Reciprocal of 1/15: 15
- Double of 1/15: 0.13333333333333
- Half of 1/15: 0.033333333333333
- Absolute value of 1/15: 0.066666666666667
Trigonometric Functions
- Sine of 1/15: 0.066617294923393
- Cosine of 1/15: 0.99777860070112
- Tangent of 1/15: 0.066765607998189
Exponential and Logarithmic Functions
- e^1/15: 1.0689391057472
- Natural log of 1/15: -2.7080502011022
Floor and Ceiling Functions
- Floor of 1/15: 0
- Ceiling of 1/15: 1
Interesting Properties and Relationships
- The sum of 1/15 and its additive inverse (-1/15) is always 0.
- The product of 1/15 and its additive inverse is: -1
- The average of 1/15 and its additive inverse is always 0.
- The distance between 1/15 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/15 = 0
The solution to this equation is x = -1/15, which is the additive inverse of 1/15.
Graphical Representation
On a coordinate plane:
- The point (1/15, 0) is reflected across the y-axis to (-1/15, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/15 and Its Additive Inverse
Consider the alternating series: 1/15 + (-1/15) + 1/15 + (-1/15) + ...
The sum of this series oscillates between 0 and 1/15, never converging unless 1/15 is 0.
In Number Theory
For integer values:
- If 1/15 is even, its additive inverse is also even.
- If 1/15 is odd, its additive inverse is also odd.
- The sum of the digits of 1/15 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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