11/14 Additive Inverse :
The additive inverse of 11/14 is -11/14.
This means that when we add 11/14 and -11/14, the result is zero:
11/14 + (-11/14) = 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: 11/14
- Additive inverse: -11/14
To verify: 11/14 + (-11/14) = 0
Extended Mathematical Exploration of 11/14
Let's explore various mathematical operations and concepts related to 11/14 and its additive inverse -11/14.
Basic Operations and Properties
- Square of 11/14: 0.61734693877551
- Cube of 11/14: 0.4850583090379
- Square root of |11/14|: 0.88640526042792
- Reciprocal of 11/14: 1.2727272727273
- Double of 11/14: 1.5714285714286
- Half of 11/14: 0.39285714285714
- Absolute value of 11/14: 0.78571428571429
Trigonometric Functions
- Sine of 11/14: 0.70733027808498
- Cosine of 11/14: 0.70688321362459
- Tangent of 11/14: 1.0006324445846
Exponential and Logarithmic Functions
- e^11/14: 2.1939735051116
- Natural log of 11/14: -0.24116205681689
Floor and Ceiling Functions
- Floor of 11/14: 0
- Ceiling of 11/14: 1
Interesting Properties and Relationships
- The sum of 11/14 and its additive inverse (-11/14) is always 0.
- The product of 11/14 and its additive inverse is: -121
- The average of 11/14 and its additive inverse is always 0.
- The distance between 11/14 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/14 = 0
The solution to this equation is x = -11/14, which is the additive inverse of 11/14.
Graphical Representation
On a coordinate plane:
- The point (11/14, 0) is reflected across the y-axis to (-11/14, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/14 and Its Additive Inverse
Consider the alternating series: 11/14 + (-11/14) + 11/14 + (-11/14) + ...
The sum of this series oscillates between 0 and 11/14, never converging unless 11/14 is 0.
In Number Theory
For integer values:
- If 11/14 is even, its additive inverse is also even.
- If 11/14 is odd, its additive inverse is also odd.
- The sum of the digits of 11/14 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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