4/11 Additive Inverse :
The additive inverse of 4/11 is -4/11.
This means that when we add 4/11 and -4/11, the result is zero:
4/11 + (-4/11) = 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: 4/11
- Additive inverse: -4/11
To verify: 4/11 + (-4/11) = 0
Extended Mathematical Exploration of 4/11
Let's explore various mathematical operations and concepts related to 4/11 and its additive inverse -4/11.
Basic Operations and Properties
- Square of 4/11: 0.13223140495868
- Cube of 4/11: 0.048084147257701
- Square root of |4/11|: 0.60302268915553
- Reciprocal of 4/11: 2.75
- Double of 4/11: 0.72727272727273
- Half of 4/11: 0.18181818181818
- Absolute value of 4/11: 0.36363636363636
Trigonometric Functions
- Sine of 4/11: 0.35567515786853
- Cosine of 4/11: 0.93460964154838
- Tangent of 4/11: 0.38056012056465
Exponential and Logarithmic Functions
- e^4/11: 1.4385510095777
- Natural log of 4/11: -1.0116009116785
Floor and Ceiling Functions
- Floor of 4/11: 0
- Ceiling of 4/11: 1
Interesting Properties and Relationships
- The sum of 4/11 and its additive inverse (-4/11) is always 0.
- The product of 4/11 and its additive inverse is: -16
- The average of 4/11 and its additive inverse is always 0.
- The distance between 4/11 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4/11 = 0
The solution to this equation is x = -4/11, which is the additive inverse of 4/11.
Graphical Representation
On a coordinate plane:
- The point (4/11, 0) is reflected across the y-axis to (-4/11, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4/11 and Its Additive Inverse
Consider the alternating series: 4/11 + (-4/11) + 4/11 + (-4/11) + ...
The sum of this series oscillates between 0 and 4/11, never converging unless 4/11 is 0.
In Number Theory
For integer values:
- If 4/11 is even, its additive inverse is also even.
- If 4/11 is odd, its additive inverse is also odd.
- The sum of the digits of 4/11 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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