11/12 Additive Inverse :
The additive inverse of 11/12 is -11/12.
This means that when we add 11/12 and -11/12, the result is zero:
11/12 + (-11/12) = 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: 11/12
- Additive inverse: -11/12
To verify: 11/12 + (-11/12) = 0
Extended Mathematical Exploration of 11/12
Let's explore various mathematical operations and concepts related to 11/12 and its additive inverse -11/12.
Basic Operations and Properties
- Square of 11/12: 0.84027777777778
- Cube of 11/12: 0.77025462962963
- Square root of |11/12|: 0.95742710775634
- Reciprocal of 11/12: 1.0909090909091
- Double of 11/12: 1.8333333333333
- Half of 11/12: 0.45833333333333
- Absolute value of 11/12: 0.91666666666667
Trigonometric Functions
- Sine of 11/12: 0.79357780324894
- Cosine of 11/12: 0.60846879146805
- Tangent of 11/12: 1.3042210453132
Exponential and Logarithmic Functions
- e^11/12: 2.5009400136621
- Natural log of 11/12: -0.08701137698963
Floor and Ceiling Functions
- Floor of 11/12: 0
- Ceiling of 11/12: 1
Interesting Properties and Relationships
- The sum of 11/12 and its additive inverse (-11/12) is always 0.
- The product of 11/12 and its additive inverse is: -121
- The average of 11/12 and its additive inverse is always 0.
- The distance between 11/12 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/12 = 0
The solution to this equation is x = -11/12, which is the additive inverse of 11/12.
Graphical Representation
On a coordinate plane:
- The point (11/12, 0) is reflected across the y-axis to (-11/12, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/12 and Its Additive Inverse
Consider the alternating series: 11/12 + (-11/12) + 11/12 + (-11/12) + ...
The sum of this series oscillates between 0 and 11/12, never converging unless 11/12 is 0.
In Number Theory
For integer values:
- If 11/12 is even, its additive inverse is also even.
- If 11/12 is odd, its additive inverse is also odd.
- The sum of the digits of 11/12 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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