1/6 Additive Inverse :
The additive inverse of 1/6 is -1/6.
This means that when we add 1/6 and -1/6, the result is zero:
1/6 + (-1/6) = 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: 1/6
- Additive inverse: -1/6
To verify: 1/6 + (-1/6) = 0
Extended Mathematical Exploration of 1/6
Let's explore various mathematical operations and concepts related to 1/6 and its additive inverse -1/6.
Basic Operations and Properties
- Square of 1/6: 0.027777777777778
- Cube of 1/6: 0.0046296296296296
- Square root of |1/6|: 0.40824829046386
- Reciprocal of 1/6: 6
- Double of 1/6: 0.33333333333333
- Half of 1/6: 0.083333333333333
- Absolute value of 1/6: 0.16666666666667
Trigonometric Functions
- Sine of 1/6: 0.16589613269342
- Cosine of 1/6: 0.98614323156293
- Tangent of 1/6: 0.16822721830224
Exponential and Logarithmic Functions
- e^1/6: 1.1813604128656
- Natural log of 1/6: -1.7917594692281
Floor and Ceiling Functions
- Floor of 1/6: 0
- Ceiling of 1/6: 1
Interesting Properties and Relationships
- The sum of 1/6 and its additive inverse (-1/6) is always 0.
- The product of 1/6 and its additive inverse is: -1
- The average of 1/6 and its additive inverse is always 0.
- The distance between 1/6 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/6 = 0
The solution to this equation is x = -1/6, which is the additive inverse of 1/6.
Graphical Representation
On a coordinate plane:
- The point (1/6, 0) is reflected across the y-axis to (-1/6, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/6 and Its Additive Inverse
Consider the alternating series: 1/6 + (-1/6) + 1/6 + (-1/6) + ...
The sum of this series oscillates between 0 and 1/6, never converging unless 1/6 is 0.
In Number Theory
For integer values:
- If 1/6 is even, its additive inverse is also even.
- If 1/6 is odd, its additive inverse is also odd.
- The sum of the digits of 1/6 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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