64/67 Additive Inverse :
The additive inverse of 64/67 is -64/67.
This means that when we add 64/67 and -64/67, the result is zero:
64/67 + (-64/67) = 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: 64/67
- Additive inverse: -64/67
To verify: 64/67 + (-64/67) = 0
Extended Mathematical Exploration of 64/67
Let's explore various mathematical operations and concepts related to 64/67 and its additive inverse -64/67.
Basic Operations and Properties
- Square of 64/67: 0.91245266206282
- Cube of 64/67: 0.87159657271672
- Square root of |64/67|: 0.97735555485044
- Reciprocal of 64/67: 1.046875
- Double of 64/67: 1.910447761194
- Half of 64/67: 0.47761194029851
- Absolute value of 64/67: 0.95522388059701
Trigonometric Functions
- Sine of 64/67: 0.8164430353803
- Cosine of 64/67: 0.57742598658096
- Tangent of 64/67: 1.4139353862728
Exponential and Logarithmic Functions
- e^64/67: 2.5992524399719
- Natural log of 64/67: -0.045809536031294
Floor and Ceiling Functions
- Floor of 64/67: 0
- Ceiling of 64/67: 1
Interesting Properties and Relationships
- The sum of 64/67 and its additive inverse (-64/67) is always 0.
- The product of 64/67 and its additive inverse is: -4096
- The average of 64/67 and its additive inverse is always 0.
- The distance between 64/67 and its additive inverse on a number line is: 128
Applications in Algebra
Consider the equation: x + 64/67 = 0
The solution to this equation is x = -64/67, which is the additive inverse of 64/67.
Graphical Representation
On a coordinate plane:
- The point (64/67, 0) is reflected across the y-axis to (-64/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 64/67 and Its Additive Inverse
Consider the alternating series: 64/67 + (-64/67) + 64/67 + (-64/67) + ...
The sum of this series oscillates between 0 and 64/67, never converging unless 64/67 is 0.
In Number Theory
For integer values:
- If 64/67 is even, its additive inverse is also even.
- If 64/67 is odd, its additive inverse is also odd.
- The sum of the digits of 64/67 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: