4/14 Additive Inverse :
The additive inverse of 4/14 is -4/14.
This means that when we add 4/14 and -4/14, the result is zero:
4/14 + (-4/14) = 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: 4/14
- Additive inverse: -4/14
To verify: 4/14 + (-4/14) = 0
Extended Mathematical Exploration of 4/14
Let's explore various mathematical operations and concepts related to 4/14 and its additive inverse -4/14.
Basic Operations and Properties
- Square of 4/14: 0.081632653061224
- Cube of 4/14: 0.02332361516035
- Square root of |4/14|: 0.53452248382485
- Reciprocal of 4/14: 3.5
- Double of 4/14: 0.57142857142857
- Half of 4/14: 0.14285714285714
- Absolute value of 4/14: 0.28571428571429
Trigonometric Functions
- Sine of 4/14: 0.28184285212221
- Cosine of 4/14: 0.95946058111192
- Tangent of 4/14: 0.29375136161986
Exponential and Logarithmic Functions
- e^4/14: 1.3307121974473
- Natural log of 4/14: -1.2527629684954
Floor and Ceiling Functions
- Floor of 4/14: 0
- Ceiling of 4/14: 1
Interesting Properties and Relationships
- The sum of 4/14 and its additive inverse (-4/14) is always 0.
- The product of 4/14 and its additive inverse is: -16
- The average of 4/14 and its additive inverse is always 0.
- The distance between 4/14 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4/14 = 0
The solution to this equation is x = -4/14, which is the additive inverse of 4/14.
Graphical Representation
On a coordinate plane:
- The point (4/14, 0) is reflected across the y-axis to (-4/14, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4/14 and Its Additive Inverse
Consider the alternating series: 4/14 + (-4/14) + 4/14 + (-4/14) + ...
The sum of this series oscillates between 0 and 4/14, never converging unless 4/14 is 0.
In Number Theory
For integer values:
- If 4/14 is even, its additive inverse is also even.
- If 4/14 is odd, its additive inverse is also odd.
- The sum of the digits of 4/14 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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