11/21 Additive Inverse :
The additive inverse of 11/21 is -11/21.
This means that when we add 11/21 and -11/21, the result is zero:
11/21 + (-11/21) = 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: 11/21
- Additive inverse: -11/21
To verify: 11/21 + (-11/21) = 0
Extended Mathematical Exploration of 11/21
Let's explore various mathematical operations and concepts related to 11/21 and its additive inverse -11/21.
Basic Operations and Properties
- Square of 11/21: 0.27437641723356
- Cube of 11/21: 0.14372098045567
- Square root of |11/21|: 0.72374686445575
- Reciprocal of 11/21: 1.9090909090909
- Double of 11/21: 1.047619047619
- Half of 11/21: 0.26190476190476
- Absolute value of 11/21: 0.52380952380952
Trigonometric Functions
- Sine of 11/21: 0.50018250219967
- Cosine of 11/21: 0.86592001044743
- Tangent of 11/21: 0.57763130100345
Exponential and Logarithmic Functions
- e^11/21: 1.6884475947814
- Natural log of 11/21: -0.64662716492505
Floor and Ceiling Functions
- Floor of 11/21: 0
- Ceiling of 11/21: 1
Interesting Properties and Relationships
- The sum of 11/21 and its additive inverse (-11/21) is always 0.
- The product of 11/21 and its additive inverse is: -121
- The average of 11/21 and its additive inverse is always 0.
- The distance between 11/21 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/21 = 0
The solution to this equation is x = -11/21, which is the additive inverse of 11/21.
Graphical Representation
On a coordinate plane:
- The point (11/21, 0) is reflected across the y-axis to (-11/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/21 and Its Additive Inverse
Consider the alternating series: 11/21 + (-11/21) + 11/21 + (-11/21) + ...
The sum of this series oscillates between 0 and 11/21, never converging unless 11/21 is 0.
In Number Theory
For integer values:
- If 11/21 is even, its additive inverse is also even.
- If 11/21 is odd, its additive inverse is also odd.
- The sum of the digits of 11/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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