63/67 Additive Inverse :
The additive inverse of 63/67 is -63/67.
This means that when we add 63/67 and -63/67, the result is zero:
63/67 + (-63/67) = 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: 63/67
- Additive inverse: -63/67
To verify: 63/67 + (-63/67) = 0
Extended Mathematical Exploration of 63/67
Let's explore various mathematical operations and concepts related to 63/67 and its additive inverse -63/67.
Basic Operations and Properties
- Square of 63/67: 0.88416128313656
- Cube of 63/67: 0.8313755348896
- Square root of |63/67|: 0.96968990273318
- Reciprocal of 63/67: 1.0634920634921
- Double of 63/67: 1.8805970149254
- Half of 63/67: 0.47014925373134
- Absolute value of 63/67: 0.94029850746269
Trigonometric Functions
- Sine of 63/67: 0.80773412054995
- Cosine of 63/67: 0.58954693663812
- Tangent of 63/67: 1.3700929821738
Exponential and Logarithmic Functions
- e^63/67: 2.5607457059541
- Natural log of 63/67: -0.061557892999433
Floor and Ceiling Functions
- Floor of 63/67: 0
- Ceiling of 63/67: 1
Interesting Properties and Relationships
- The sum of 63/67 and its additive inverse (-63/67) is always 0.
- The product of 63/67 and its additive inverse is: -3969
- The average of 63/67 and its additive inverse is always 0.
- The distance between 63/67 and its additive inverse on a number line is: 126
Applications in Algebra
Consider the equation: x + 63/67 = 0
The solution to this equation is x = -63/67, which is the additive inverse of 63/67.
Graphical Representation
On a coordinate plane:
- The point (63/67, 0) is reflected across the y-axis to (-63/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 63/67 and Its Additive Inverse
Consider the alternating series: 63/67 + (-63/67) + 63/67 + (-63/67) + ...
The sum of this series oscillates between 0 and 63/67, never converging unless 63/67 is 0.
In Number Theory
For integer values:
- If 63/67 is even, its additive inverse is also even.
- If 63/67 is odd, its additive inverse is also odd.
- The sum of the digits of 63/67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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