71/81 Additive Inverse :
The additive inverse of 71/81 is -71/81.
This means that when we add 71/81 and -71/81, the result is zero:
71/81 + (-71/81) = 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: 71/81
- Additive inverse: -71/81
To verify: 71/81 + (-71/81) = 0
Extended Mathematical Exploration of 71/81
Let's explore various mathematical operations and concepts related to 71/81 and its additive inverse -71/81.
Basic Operations and Properties
- Square of 71/81: 0.76832799878067
- Cube of 71/81: 0.67347269028923
- Square root of |71/81|: 0.93623886368626
- Reciprocal of 71/81: 1.1408450704225
- Double of 71/81: 1.7530864197531
- Half of 71/81: 0.43827160493827
- Absolute value of 71/81: 0.87654320987654
Trigonometric Functions
- Sine of 71/81: 0.76853178057477
- Cosine of 71/81: 0.63981161465433
- Tangent of 71/81: 1.2011844783249
Exponential and Logarithmic Functions
- e^71/81: 2.4025801199401
- Natural log of 71/81: -0.13176927763112
Floor and Ceiling Functions
- Floor of 71/81: 0
- Ceiling of 71/81: 1
Interesting Properties and Relationships
- The sum of 71/81 and its additive inverse (-71/81) is always 0.
- The product of 71/81 and its additive inverse is: -5041
- The average of 71/81 and its additive inverse is always 0.
- The distance between 71/81 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/81 = 0
The solution to this equation is x = -71/81, which is the additive inverse of 71/81.
Graphical Representation
On a coordinate plane:
- The point (71/81, 0) is reflected across the y-axis to (-71/81, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/81 and Its Additive Inverse
Consider the alternating series: 71/81 + (-71/81) + 71/81 + (-71/81) + ...
The sum of this series oscillates between 0 and 71/81, never converging unless 71/81 is 0.
In Number Theory
For integer values:
- If 71/81 is even, its additive inverse is also even.
- If 71/81 is odd, its additive inverse is also odd.
- The sum of the digits of 71/81 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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