64/78 Additive Inverse :
The additive inverse of 64/78 is -64/78.
This means that when we add 64/78 and -64/78, the result is zero:
64/78 + (-64/78) = 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: 64/78
- Additive inverse: -64/78
To verify: 64/78 + (-64/78) = 0
Extended Mathematical Exploration of 64/78
Let's explore various mathematical operations and concepts related to 64/78 and its additive inverse -64/78.
Basic Operations and Properties
- Square of 64/78: 0.6732412886259
- Cube of 64/78: 0.55240310861613
- Square root of |64/78|: 0.90582162731568
- Reciprocal of 64/78: 1.21875
- Double of 64/78: 1.6410256410256
- Half of 64/78: 0.41025641025641
- Absolute value of 64/78: 0.82051282051282
Trigonometric Functions
- Sine of 64/78: 0.73149559060079
- Cosine of 64/78: 0.68184617101777
- Tangent of 64/78: 1.0728161595583
Exponential and Logarithmic Functions
- e^64/78: 2.2716644950281
- Natural log of 64/78: -0.19782574332992
Floor and Ceiling Functions
- Floor of 64/78: 0
- Ceiling of 64/78: 1
Interesting Properties and Relationships
- The sum of 64/78 and its additive inverse (-64/78) is always 0.
- The product of 64/78 and its additive inverse is: -4096
- The average of 64/78 and its additive inverse is always 0.
- The distance between 64/78 and its additive inverse on a number line is: 128
Applications in Algebra
Consider the equation: x + 64/78 = 0
The solution to this equation is x = -64/78, which is the additive inverse of 64/78.
Graphical Representation
On a coordinate plane:
- The point (64/78, 0) is reflected across the y-axis to (-64/78, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 64/78 and Its Additive Inverse
Consider the alternating series: 64/78 + (-64/78) + 64/78 + (-64/78) + ...
The sum of this series oscillates between 0 and 64/78, never converging unless 64/78 is 0.
In Number Theory
For integer values:
- If 64/78 is even, its additive inverse is also even.
- If 64/78 is odd, its additive inverse is also odd.
- The sum of the digits of 64/78 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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