63/75 Additive Inverse :
The additive inverse of 63/75 is -63/75.
This means that when we add 63/75 and -63/75, the result is zero:
63/75 + (-63/75) = 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: 63/75
- Additive inverse: -63/75
To verify: 63/75 + (-63/75) = 0
Extended Mathematical Exploration of 63/75
Let's explore various mathematical operations and concepts related to 63/75 and its additive inverse -63/75.
Basic Operations and Properties
- Square of 63/75: 0.7056
- Cube of 63/75: 0.592704
- Square root of |63/75|: 0.91651513899117
- Reciprocal of 63/75: 1.1904761904762
- Double of 63/75: 1.68
- Half of 63/75: 0.42
- Absolute value of 63/75: 0.84
Trigonometric Functions
- Sine of 63/75: 0.74464311997086
- Cosine of 63/75: 0.66746282584131
- Tangent of 63/75: 1.1156323485615
Exponential and Logarithmic Functions
- e^63/75: 2.3163669767811
- Natural log of 63/75: -0.17435338714478
Floor and Ceiling Functions
- Floor of 63/75: 0
- Ceiling of 63/75: 1
Interesting Properties and Relationships
- The sum of 63/75 and its additive inverse (-63/75) is always 0.
- The product of 63/75 and its additive inverse is: -3969
- The average of 63/75 and its additive inverse is always 0.
- The distance between 63/75 and its additive inverse on a number line is: 126
Applications in Algebra
Consider the equation: x + 63/75 = 0
The solution to this equation is x = -63/75, which is the additive inverse of 63/75.
Graphical Representation
On a coordinate plane:
- The point (63/75, 0) is reflected across the y-axis to (-63/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 63/75 and Its Additive Inverse
Consider the alternating series: 63/75 + (-63/75) + 63/75 + (-63/75) + ...
The sum of this series oscillates between 0 and 63/75, never converging unless 63/75 is 0.
In Number Theory
For integer values:
- If 63/75 is even, its additive inverse is also even.
- If 63/75 is odd, its additive inverse is also odd.
- The sum of the digits of 63/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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