71/83 Additive Inverse :
The additive inverse of 71/83 is -71/83.
This means that when we add 71/83 and -71/83, the result is zero:
71/83 + (-71/83) = 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: 71/83
- Additive inverse: -71/83
To verify: 71/83 + (-71/83) = 0
Extended Mathematical Exploration of 71/83
Let's explore various mathematical operations and concepts related to 71/83 and its additive inverse -71/83.
Basic Operations and Properties
- Square of 71/83: 0.73174626215706
- Cube of 71/83: 0.6259516218452
- Square root of |71/83|: 0.924890094415
- Reciprocal of 71/83: 1.169014084507
- Double of 71/83: 1.710843373494
- Half of 71/83: 0.42771084337349
- Absolute value of 71/83: 0.85542168674699
Trigonometric Functions
- Sine of 71/83: 0.75484756768628
- Cosine of 71/83: 0.65590025884894
- Tangent of 71/83: 1.1508572492577
Exponential and Logarithmic Functions
- e^71/83: 2.3523661330781
- Natural log of 71/83: -0.15616073075528
Floor and Ceiling Functions
- Floor of 71/83: 0
- Ceiling of 71/83: 1
Interesting Properties and Relationships
- The sum of 71/83 and its additive inverse (-71/83) is always 0.
- The product of 71/83 and its additive inverse is: -5041
- The average of 71/83 and its additive inverse is always 0.
- The distance between 71/83 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/83 = 0
The solution to this equation is x = -71/83, which is the additive inverse of 71/83.
Graphical Representation
On a coordinate plane:
- The point (71/83, 0) is reflected across the y-axis to (-71/83, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/83 and Its Additive Inverse
Consider the alternating series: 71/83 + (-71/83) + 71/83 + (-71/83) + ...
The sum of this series oscillates between 0 and 71/83, never converging unless 71/83 is 0.
In Number Theory
For integer values:
- If 71/83 is even, its additive inverse is also even.
- If 71/83 is odd, its additive inverse is also odd.
- The sum of the digits of 71/83 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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