64/75 Additive Inverse :
The additive inverse of 64/75 is -64/75.
This means that when we add 64/75 and -64/75, the result is zero:
64/75 + (-64/75) = 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: 64/75
- Additive inverse: -64/75
To verify: 64/75 + (-64/75) = 0
Extended Mathematical Exploration of 64/75
Let's explore various mathematical operations and concepts related to 64/75 and its additive inverse -64/75.
Basic Operations and Properties
- Square of 64/75: 0.72817777777778
- Cube of 64/75: 0.62137837037037
- Square root of |64/75|: 0.9237604307034
- Reciprocal of 64/75: 1.171875
- Double of 64/75: 1.7066666666667
- Half of 64/75: 0.42666666666667
- Absolute value of 64/75: 0.85333333333333
Trigonometric Functions
- Sine of 64/75: 0.75347617110978
- Cosine of 64/75: 0.65747521593574
- Tangent of 64/75: 1.1460145612294
Exponential and Logarithmic Functions
- e^64/75: 2.3474586872581
- Natural log of 64/75: -0.15860503017664
Floor and Ceiling Functions
- Floor of 64/75: 0
- Ceiling of 64/75: 1
Interesting Properties and Relationships
- The sum of 64/75 and its additive inverse (-64/75) is always 0.
- The product of 64/75 and its additive inverse is: -4096
- The average of 64/75 and its additive inverse is always 0.
- The distance between 64/75 and its additive inverse on a number line is: 128
Applications in Algebra
Consider the equation: x + 64/75 = 0
The solution to this equation is x = -64/75, which is the additive inverse of 64/75.
Graphical Representation
On a coordinate plane:
- The point (64/75, 0) is reflected across the y-axis to (-64/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 64/75 and Its Additive Inverse
Consider the alternating series: 64/75 + (-64/75) + 64/75 + (-64/75) + ...
The sum of this series oscillates between 0 and 64/75, never converging unless 64/75 is 0.
In Number Theory
For integer values:
- If 64/75 is even, its additive inverse is also even.
- If 64/75 is odd, its additive inverse is also odd.
- The sum of the digits of 64/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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