67/75 Additive Inverse :
The additive inverse of 67/75 is -67/75.
This means that when we add 67/75 and -67/75, the result is zero:
67/75 + (-67/75) = 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: 67/75
- Additive inverse: -67/75
To verify: 67/75 + (-67/75) = 0
Extended Mathematical Exploration of 67/75
Let's explore various mathematical operations and concepts related to 67/75 and its additive inverse -67/75.
Basic Operations and Properties
- Square of 67/75: 0.79804444444444
- Cube of 67/75: 0.7129197037037
- Square root of |67/75|: 0.94516312525052
- Reciprocal of 67/75: 1.1194029850746
- Double of 67/75: 1.7866666666667
- Half of 67/75: 0.44666666666667
- Absolute value of 67/75: 0.89333333333333
Trigonometric Functions
- Sine of 67/75: 0.77916546666888
- Cosine of 67/75: 0.62681829548177
- Tangent of 67/75: 1.2430483798658
Exponential and Logarithmic Functions
- e^67/75: 2.4432602936698
- Natural log of 67/75: -0.11279549414534
Floor and Ceiling Functions
- Floor of 67/75: 0
- Ceiling of 67/75: 1
Interesting Properties and Relationships
- The sum of 67/75 and its additive inverse (-67/75) is always 0.
- The product of 67/75 and its additive inverse is: -4489
- The average of 67/75 and its additive inverse is always 0.
- The distance between 67/75 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/75 = 0
The solution to this equation is x = -67/75, which is the additive inverse of 67/75.
Graphical Representation
On a coordinate plane:
- The point (67/75, 0) is reflected across the y-axis to (-67/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/75 and Its Additive Inverse
Consider the alternating series: 67/75 + (-67/75) + 67/75 + (-67/75) + ...
The sum of this series oscillates between 0 and 67/75, never converging unless 67/75 is 0.
In Number Theory
For integer values:
- If 67/75 is even, its additive inverse is also even.
- If 67/75 is odd, its additive inverse is also odd.
- The sum of the digits of 67/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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