71/80 Additive Inverse :
The additive inverse of 71/80 is -71/80.
This means that when we add 71/80 and -71/80, the result is zero:
71/80 + (-71/80) = 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: 71/80
- Additive inverse: -71/80
To verify: 71/80 + (-71/80) = 0
Extended Mathematical Exploration of 71/80
Let's explore various mathematical operations and concepts related to 71/80 and its additive inverse -71/80.
Basic Operations and Properties
- Square of 71/80: 0.78765625
- Cube of 71/80: 0.699044921875
- Square root of |71/80|: 0.94207218407084
- Reciprocal of 71/80: 1.1267605633803
- Double of 71/80: 1.775
- Half of 71/80: 0.44375
- Absolute value of 71/80: 0.8875
Trigonometric Functions
- Sine of 71/80: 0.77549579075154
- Cosine of 71/80: 0.63135273700733
- Tangent of 71/80: 1.2283082741154
Exponential and Logarithmic Functions
- e^71/80: 2.4290494306043
- Natural log of 71/80: -0.11934675763257
Floor and Ceiling Functions
- Floor of 71/80: 0
- Ceiling of 71/80: 1
Interesting Properties and Relationships
- The sum of 71/80 and its additive inverse (-71/80) is always 0.
- The product of 71/80 and its additive inverse is: -5041
- The average of 71/80 and its additive inverse is always 0.
- The distance between 71/80 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/80 = 0
The solution to this equation is x = -71/80, which is the additive inverse of 71/80.
Graphical Representation
On a coordinate plane:
- The point (71/80, 0) is reflected across the y-axis to (-71/80, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/80 and Its Additive Inverse
Consider the alternating series: 71/80 + (-71/80) + 71/80 + (-71/80) + ...
The sum of this series oscillates between 0 and 71/80, never converging unless 71/80 is 0.
In Number Theory
For integer values:
- If 71/80 is even, its additive inverse is also even.
- If 71/80 is odd, its additive inverse is also odd.
- The sum of the digits of 71/80 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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