68/75 Additive Inverse :
The additive inverse of 68/75 is -68/75.
This means that when we add 68/75 and -68/75, the result is zero:
68/75 + (-68/75) = 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: 68/75
- Additive inverse: -68/75
To verify: 68/75 + (-68/75) = 0
Extended Mathematical Exploration of 68/75
Let's explore various mathematical operations and concepts related to 68/75 and its additive inverse -68/75.
Basic Operations and Properties
- Square of 68/75: 0.82204444444444
- Cube of 68/75: 0.7453202962963
- Square root of |68/75|: 0.95219045713905
- Reciprocal of 68/75: 1.1029411764706
- Double of 68/75: 1.8133333333333
- Half of 68/75: 0.45333333333333
- Absolute value of 68/75: 0.90666666666667
Trigonometric Functions
- Sine of 68/75: 0.78745353818571
- Cosine of 68/75: 0.61637401405218
- Tangent of 68/75: 1.2775579765422
Exponential and Logarithmic Functions
- e^68/75: 2.4760552447428
- Natural log of 68/75: -0.097980408360204
Floor and Ceiling Functions
- Floor of 68/75: 0
- Ceiling of 68/75: 1
Interesting Properties and Relationships
- The sum of 68/75 and its additive inverse (-68/75) is always 0.
- The product of 68/75 and its additive inverse is: -4624
- The average of 68/75 and its additive inverse is always 0.
- The distance between 68/75 and its additive inverse on a number line is: 136
Applications in Algebra
Consider the equation: x + 68/75 = 0
The solution to this equation is x = -68/75, which is the additive inverse of 68/75.
Graphical Representation
On a coordinate plane:
- The point (68/75, 0) is reflected across the y-axis to (-68/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 68/75 and Its Additive Inverse
Consider the alternating series: 68/75 + (-68/75) + 68/75 + (-68/75) + ...
The sum of this series oscillates between 0 and 68/75, never converging unless 68/75 is 0.
In Number Theory
For integer values:
- If 68/75 is even, its additive inverse is also even.
- If 68/75 is odd, its additive inverse is also odd.
- The sum of the digits of 68/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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