58/67 Additive Inverse :
The additive inverse of 58/67 is -58/67.
This means that when we add 58/67 and -58/67, the result is zero:
58/67 + (-58/67) = 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: 58/67
- Additive inverse: -58/67
To verify: 58/67 + (-58/67) = 0
Extended Mathematical Exploration of 58/67
Let's explore various mathematical operations and concepts related to 58/67 and its additive inverse -58/67.
Basic Operations and Properties
- Square of 58/67: 0.7493873914012
- Cube of 58/67: 0.64872341345179
- Square root of |58/67|: 0.93041476868709
- Reciprocal of 58/67: 1.1551724137931
- Double of 58/67: 1.7313432835821
- Half of 58/67: 0.43283582089552
- Absolute value of 58/67: 0.86567164179104
Trigonometric Functions
- Sine of 58/67: 0.7615307457416
- Cosine of 58/67: 0.64812878603735
- Tangent of 58/67: 1.1749682503652
Exponential and Logarithmic Functions
- e^58/67: 2.3766017751242
- Natural log of 58/67: -0.14424960884455
Floor and Ceiling Functions
- Floor of 58/67: 0
- Ceiling of 58/67: 1
Interesting Properties and Relationships
- The sum of 58/67 and its additive inverse (-58/67) is always 0.
- The product of 58/67 and its additive inverse is: -3364
- The average of 58/67 and its additive inverse is always 0.
- The distance between 58/67 and its additive inverse on a number line is: 116
Applications in Algebra
Consider the equation: x + 58/67 = 0
The solution to this equation is x = -58/67, which is the additive inverse of 58/67.
Graphical Representation
On a coordinate plane:
- The point (58/67, 0) is reflected across the y-axis to (-58/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 58/67 and Its Additive Inverse
Consider the alternating series: 58/67 + (-58/67) + 58/67 + (-58/67) + ...
The sum of this series oscillates between 0 and 58/67, never converging unless 58/67 is 0.
In Number Theory
For integer values:
- If 58/67 is even, its additive inverse is also even.
- If 58/67 is odd, its additive inverse is also odd.
- The sum of the digits of 58/67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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