6/7 Additive Inverse :
The additive inverse of 6/7 is -6/7.
This means that when we add 6/7 and -6/7, the result is zero:
6/7 + (-6/7) = 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: 6/7
- Additive inverse: -6/7
To verify: 6/7 + (-6/7) = 0
Extended Mathematical Exploration of 6/7
Let's explore various mathematical operations and concepts related to 6/7 and its additive inverse -6/7.
Basic Operations and Properties
- Square of 6/7: 0.73469387755102
- Cube of 6/7: 0.62973760932945
- Square root of |6/7|: 0.92582009977255
- Reciprocal of 6/7: 1.1666666666667
- Double of 6/7: 1.7142857142857
- Half of 6/7: 0.42857142857143
- Absolute value of 6/7: 0.85714285714286
Trigonometric Functions
- Sine of 6/7: 0.75597536514673
- Cosine of 6/7: 0.65460006667527
- Tangent of 6/7: 1.1548660069443
Exponential and Logarithmic Functions
- e^6/7: 2.3564184423837
- Natural log of 6/7: -0.15415067982726
Floor and Ceiling Functions
- Floor of 6/7: 0
- Ceiling of 6/7: 1
Interesting Properties and Relationships
- The sum of 6/7 and its additive inverse (-6/7) is always 0.
- The product of 6/7 and its additive inverse is: -36
- The average of 6/7 and its additive inverse is always 0.
- The distance between 6/7 and its additive inverse on a number line is: 12
Applications in Algebra
Consider the equation: x + 6/7 = 0
The solution to this equation is x = -6/7, which is the additive inverse of 6/7.
Graphical Representation
On a coordinate plane:
- The point (6/7, 0) is reflected across the y-axis to (-6/7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 6/7 and Its Additive Inverse
Consider the alternating series: 6/7 + (-6/7) + 6/7 + (-6/7) + ...
The sum of this series oscillates between 0 and 6/7, never converging unless 6/7 is 0.
In Number Theory
For integer values:
- If 6/7 is even, its additive inverse is also even.
- If 6/7 is odd, its additive inverse is also odd.
- The sum of the digits of 6/7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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