1/7 Additive Inverse :
The additive inverse of 1/7 is -1/7.
This means that when we add 1/7 and -1/7, the result is zero:
1/7 + (-1/7) = 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: 1/7
- Additive inverse: -1/7
To verify: 1/7 + (-1/7) = 0
Extended Mathematical Exploration of 1/7
Let's explore various mathematical operations and concepts related to 1/7 and its additive inverse -1/7.
Basic Operations and Properties
- Square of 1/7: 0.020408163265306
- Cube of 1/7: 0.0029154518950437
- Square root of |1/7|: 0.37796447300923
- Reciprocal of 1/7: 7
- Double of 1/7: 0.28571428571429
- Half of 1/7: 0.071428571428571
- Absolute value of 1/7: 0.14285714285714
Trigonometric Functions
- Sine of 1/7: 0.14237172979226
- Cosine of 1/7: 0.98981326044662
- Tangent of 1/7: 0.14383695943619
Exponential and Logarithmic Functions
- e^1/7: 1.1535649948951
- Natural log of 1/7: -1.9459101490553
Floor and Ceiling Functions
- Floor of 1/7: 0
- Ceiling of 1/7: 1
Interesting Properties and Relationships
- The sum of 1/7 and its additive inverse (-1/7) is always 0.
- The product of 1/7 and its additive inverse is: -1
- The average of 1/7 and its additive inverse is always 0.
- The distance between 1/7 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/7 = 0
The solution to this equation is x = -1/7, which is the additive inverse of 1/7.
Graphical Representation
On a coordinate plane:
- The point (1/7, 0) is reflected across the y-axis to (-1/7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/7 and Its Additive Inverse
Consider the alternating series: 1/7 + (-1/7) + 1/7 + (-1/7) + ...
The sum of this series oscillates between 0 and 1/7, never converging unless 1/7 is 0.
In Number Theory
For integer values:
- If 1/7 is even, its additive inverse is also even.
- If 1/7 is odd, its additive inverse is also odd.
- The sum of the digits of 1/7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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