2/7 Additive Inverse :
The additive inverse of 2/7 is -2/7.
This means that when we add 2/7 and -2/7, the result is zero:
2/7 + (-2/7) = 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: 2/7
- Additive inverse: -2/7
To verify: 2/7 + (-2/7) = 0
Extended Mathematical Exploration of 2/7
Let's explore various mathematical operations and concepts related to 2/7 and its additive inverse -2/7.
Basic Operations and Properties
- Square of 2/7: 0.081632653061224
- Cube of 2/7: 0.02332361516035
- Square root of |2/7|: 0.53452248382485
- Reciprocal of 2/7: 3.5
- Double of 2/7: 0.57142857142857
- Half of 2/7: 0.14285714285714
- Absolute value of 2/7: 0.28571428571429
Trigonometric Functions
- Sine of 2/7: 0.28184285212221
- Cosine of 2/7: 0.95946058111192
- Tangent of 2/7: 0.29375136161986
Exponential and Logarithmic Functions
- e^2/7: 1.3307121974473
- Natural log of 2/7: -1.2527629684954
Floor and Ceiling Functions
- Floor of 2/7: 0
- Ceiling of 2/7: 1
Interesting Properties and Relationships
- The sum of 2/7 and its additive inverse (-2/7) is always 0.
- The product of 2/7 and its additive inverse is: -4
- The average of 2/7 and its additive inverse is always 0.
- The distance between 2/7 and its additive inverse on a number line is: 4
Applications in Algebra
Consider the equation: x + 2/7 = 0
The solution to this equation is x = -2/7, which is the additive inverse of 2/7.
Graphical Representation
On a coordinate plane:
- The point (2/7, 0) is reflected across the y-axis to (-2/7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 2/7 and Its Additive Inverse
Consider the alternating series: 2/7 + (-2/7) + 2/7 + (-2/7) + ...
The sum of this series oscillates between 0 and 2/7, never converging unless 2/7 is 0.
In Number Theory
For integer values:
- If 2/7 is even, its additive inverse is also even.
- If 2/7 is odd, its additive inverse is also odd.
- The sum of the digits of 2/7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: