5/6 Additive Inverse :
The additive inverse of 5/6 is -5/6.
This means that when we add 5/6 and -5/6, the result is zero:
5/6 + (-5/6) = 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: 5/6
- Additive inverse: -5/6
To verify: 5/6 + (-5/6) = 0
Extended Mathematical Exploration of 5/6
Let's explore various mathematical operations and concepts related to 5/6 and its additive inverse -5/6.
Basic Operations and Properties
- Square of 5/6: 0.69444444444444
- Cube of 5/6: 0.5787037037037
- Square root of |5/6|: 0.91287092917528
- Reciprocal of 5/6: 1.2
- Double of 5/6: 1.6666666666667
- Half of 5/6: 0.41666666666667
- Absolute value of 5/6: 0.83333333333333
Trigonometric Functions
- Sine of 5/6: 0.74017685319604
- Cosine of 5/6: 0.67241224408306
- Tangent of 5/6: 1.1007783687898
Exponential and Logarithmic Functions
- e^5/6: 2.3009758908928
- Natural log of 5/6: -0.18232155679395
Floor and Ceiling Functions
- Floor of 5/6: 0
- Ceiling of 5/6: 1
Interesting Properties and Relationships
- The sum of 5/6 and its additive inverse (-5/6) is always 0.
- The product of 5/6 and its additive inverse is: -25
- The average of 5/6 and its additive inverse is always 0.
- The distance between 5/6 and its additive inverse on a number line is: 10
Applications in Algebra
Consider the equation: x + 5/6 = 0
The solution to this equation is x = -5/6, which is the additive inverse of 5/6.
Graphical Representation
On a coordinate plane:
- The point (5/6, 0) is reflected across the y-axis to (-5/6, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 5/6 and Its Additive Inverse
Consider the alternating series: 5/6 + (-5/6) + 5/6 + (-5/6) + ...
The sum of this series oscillates between 0 and 5/6, never converging unless 5/6 is 0.
In Number Theory
For integer values:
- If 5/6 is even, its additive inverse is also even.
- If 5/6 is odd, its additive inverse is also odd.
- The sum of the digits of 5/6 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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