63/64 Additive Inverse :
The additive inverse of 63/64 is -63/64.
This means that when we add 63/64 and -63/64, the result is zero:
63/64 + (-63/64) = 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: 63/64
- Additive inverse: -63/64
To verify: 63/64 + (-63/64) = 0
Extended Mathematical Exploration of 63/64
Let's explore various mathematical operations and concepts related to 63/64 and its additive inverse -63/64.
Basic Operations and Properties
- Square of 63/64: 0.968994140625
- Cube of 63/64: 0.95385360717773
- Square root of |63/64|: 0.99215674164922
- Reciprocal of 63/64: 1.015873015873
- Double of 63/64: 1.96875
- Half of 63/64: 0.4921875
- Absolute value of 63/64: 0.984375
Trigonometric Functions
- Sine of 63/64: 0.83292638825319
- Cosine of 63/64: 0.55338380148997
- Tangent of 63/64: 1.5051513723578
Exponential and Logarithmic Functions
- e^63/64: 2.6761387748945
- Natural log of 63/64: -0.015748356968139
Floor and Ceiling Functions
- Floor of 63/64: 0
- Ceiling of 63/64: 1
Interesting Properties and Relationships
- The sum of 63/64 and its additive inverse (-63/64) is always 0.
- The product of 63/64 and its additive inverse is: -3969
- The average of 63/64 and its additive inverse is always 0.
- The distance between 63/64 and its additive inverse on a number line is: 126
Applications in Algebra
Consider the equation: x + 63/64 = 0
The solution to this equation is x = -63/64, which is the additive inverse of 63/64.
Graphical Representation
On a coordinate plane:
- The point (63/64, 0) is reflected across the y-axis to (-63/64, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 63/64 and Its Additive Inverse
Consider the alternating series: 63/64 + (-63/64) + 63/64 + (-63/64) + ...
The sum of this series oscillates between 0 and 63/64, never converging unless 63/64 is 0.
In Number Theory
For integer values:
- If 63/64 is even, its additive inverse is also even.
- If 63/64 is odd, its additive inverse is also odd.
- The sum of the digits of 63/64 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: