11/22 Additive Inverse :
The additive inverse of 11/22 is -11/22.
This means that when we add 11/22 and -11/22, the result is zero:
11/22 + (-11/22) = 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: 11/22
- Additive inverse: -11/22
To verify: 11/22 + (-11/22) = 0
Extended Mathematical Exploration of 11/22
Let's explore various mathematical operations and concepts related to 11/22 and its additive inverse -11/22.
Basic Operations and Properties
- Square of 11/22: 0.25
- Cube of 11/22: 0.125
- Square root of |11/22|: 0.70710678118655
- Reciprocal of 11/22: 2
- Double of 11/22: 1
- Half of 11/22: 0.25
- Absolute value of 11/22: 0.5
Trigonometric Functions
- Sine of 11/22: 0.4794255386042
- Cosine of 11/22: 0.87758256189037
- Tangent of 11/22: 0.54630248984379
Exponential and Logarithmic Functions
- e^11/22: 1.6487212707001
- Natural log of 11/22: -0.69314718055995
Floor and Ceiling Functions
- Floor of 11/22: 0
- Ceiling of 11/22: 1
Interesting Properties and Relationships
- The sum of 11/22 and its additive inverse (-11/22) is always 0.
- The product of 11/22 and its additive inverse is: -121
- The average of 11/22 and its additive inverse is always 0.
- The distance between 11/22 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/22 = 0
The solution to this equation is x = -11/22, which is the additive inverse of 11/22.
Graphical Representation
On a coordinate plane:
- The point (11/22, 0) is reflected across the y-axis to (-11/22, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/22 and Its Additive Inverse
Consider the alternating series: 11/22 + (-11/22) + 11/22 + (-11/22) + ...
The sum of this series oscillates between 0 and 11/22, never converging unless 11/22 is 0.
In Number Theory
For integer values:
- If 11/22 is even, its additive inverse is also even.
- If 11/22 is odd, its additive inverse is also odd.
- The sum of the digits of 11/22 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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