64/71 Additive Inverse :
The additive inverse of 64/71 is -64/71.
This means that when we add 64/71 and -64/71, the result is zero:
64/71 + (-64/71) = 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: 64/71
- Additive inverse: -64/71
To verify: 64/71 + (-64/71) = 0
Extended Mathematical Exploration of 64/71
Let's explore various mathematical operations and concepts related to 64/71 and its additive inverse -64/71.
Basic Operations and Properties
- Square of 64/71: 0.81253719500099
- Cube of 64/71: 0.7324278940854
- Square root of |64/71|: 0.94942532655508
- Reciprocal of 64/71: 1.109375
- Double of 64/71: 1.8028169014085
- Half of 64/71: 0.45070422535211
- Absolute value of 64/71: 0.90140845070423
Trigonometric Functions
- Sine of 64/71: 0.78420163937984
- Cosine of 64/71: 0.62050607474381
- Tangent of 64/71: 1.2638097696362
Exponential and Logarithmic Functions
- e^64/71: 2.4630697816351
- Natural log of 64/71: -0.10379679368164
Floor and Ceiling Functions
- Floor of 64/71: 0
- Ceiling of 64/71: 1
Interesting Properties and Relationships
- The sum of 64/71 and its additive inverse (-64/71) is always 0.
- The product of 64/71 and its additive inverse is: -4096
- The average of 64/71 and its additive inverse is always 0.
- The distance between 64/71 and its additive inverse on a number line is: 128
Applications in Algebra
Consider the equation: x + 64/71 = 0
The solution to this equation is x = -64/71, which is the additive inverse of 64/71.
Graphical Representation
On a coordinate plane:
- The point (64/71, 0) is reflected across the y-axis to (-64/71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 64/71 and Its Additive Inverse
Consider the alternating series: 64/71 + (-64/71) + 64/71 + (-64/71) + ...
The sum of this series oscillates between 0 and 64/71, never converging unless 64/71 is 0.
In Number Theory
For integer values:
- If 64/71 is even, its additive inverse is also even.
- If 64/71 is odd, its additive inverse is also odd.
- The sum of the digits of 64/71 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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