64/69 Additive Inverse :
The additive inverse of 64/69 is -64/69.
This means that when we add 64/69 and -64/69, the result is zero:
64/69 + (-64/69) = 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: 64/69
- Additive inverse: -64/69
To verify: 64/69 + (-64/69) = 0
Extended Mathematical Exploration of 64/69
Let's explore various mathematical operations and concepts related to 64/69 and its additive inverse -64/69.
Basic Operations and Properties
- Square of 64/69: 0.86032346145768
- Cube of 64/69: 0.7979811816419
- Square root of |64/69|: 0.96308682468615
- Reciprocal of 64/69: 1.078125
- Double of 64/69: 1.8550724637681
- Half of 64/69: 0.46376811594203
- Absolute value of 64/69: 0.92753623188406
Trigonometric Functions
- Sine of 64/69: 0.80014458509299
- Cosine of 64/69: 0.5998071714696
- Tangent of 64/69: 1.3340030315619
Exponential and Logarithmic Functions
- e^64/69: 2.5282724208326
- Natural log of 64/69: -0.075223421237588
Floor and Ceiling Functions
- Floor of 64/69: 0
- Ceiling of 64/69: 1
Interesting Properties and Relationships
- The sum of 64/69 and its additive inverse (-64/69) is always 0.
- The product of 64/69 and its additive inverse is: -4096
- The average of 64/69 and its additive inverse is always 0.
- The distance between 64/69 and its additive inverse on a number line is: 128
Applications in Algebra
Consider the equation: x + 64/69 = 0
The solution to this equation is x = -64/69, which is the additive inverse of 64/69.
Graphical Representation
On a coordinate plane:
- The point (64/69, 0) is reflected across the y-axis to (-64/69, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 64/69 and Its Additive Inverse
Consider the alternating series: 64/69 + (-64/69) + 64/69 + (-64/69) + ...
The sum of this series oscillates between 0 and 64/69, never converging unless 64/69 is 0.
In Number Theory
For integer values:
- If 64/69 is even, its additive inverse is also even.
- If 64/69 is odd, its additive inverse is also odd.
- The sum of the digits of 64/69 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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