71/85 Additive Inverse :
The additive inverse of 71/85 is -71/85.
This means that when we add 71/85 and -71/85, the result is zero:
71/85 + (-71/85) = 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: 71/85
- Additive inverse: -71/85
To verify: 71/85 + (-71/85) = 0
Extended Mathematical Exploration of 71/85
Let's explore various mathematical operations and concepts related to 71/85 and its additive inverse -71/85.
Basic Operations and Properties
- Square of 71/85: 0.69771626297578
- Cube of 71/85: 0.58279829025036
- Square root of |71/85|: 0.91394426397186
- Reciprocal of 71/85: 1.1971830985915
- Double of 71/85: 1.6705882352941
- Half of 71/85: 0.41764705882353
- Absolute value of 71/85: 0.83529411764706
Trigonometric Functions
- Sine of 71/85: 0.74149388486244
- Cosine of 71/85: 0.67095962524701
- Tangent of 71/85: 1.1051244470775
Exponential and Logarithmic Functions
- e^71/85: 2.3054920344708
- Natural log of 71/85: -0.179971379449
Floor and Ceiling Functions
- Floor of 71/85: 0
- Ceiling of 71/85: 1
Interesting Properties and Relationships
- The sum of 71/85 and its additive inverse (-71/85) is always 0.
- The product of 71/85 and its additive inverse is: -5041
- The average of 71/85 and its additive inverse is always 0.
- The distance between 71/85 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/85 = 0
The solution to this equation is x = -71/85, which is the additive inverse of 71/85.
Graphical Representation
On a coordinate plane:
- The point (71/85, 0) is reflected across the y-axis to (-71/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/85 and Its Additive Inverse
Consider the alternating series: 71/85 + (-71/85) + 71/85 + (-71/85) + ...
The sum of this series oscillates between 0 and 71/85, never converging unless 71/85 is 0.
In Number Theory
For integer values:
- If 71/85 is even, its additive inverse is also even.
- If 71/85 is odd, its additive inverse is also odd.
- The sum of the digits of 71/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: