67/80 Additive Inverse :
The additive inverse of 67/80 is -67/80.
This means that when we add 67/80 and -67/80, the result is zero:
67/80 + (-67/80) = 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: 67/80
- Additive inverse: -67/80
To verify: 67/80 + (-67/80) = 0
Extended Mathematical Exploration of 67/80
Let's explore various mathematical operations and concepts related to 67/80 and its additive inverse -67/80.
Basic Operations and Properties
- Square of 67/80: 0.70140625
- Cube of 67/80: 0.587427734375
- Square root of |67/80|: 0.91515026088616
- Reciprocal of 67/80: 1.1940298507463
- Double of 67/80: 1.675
- Half of 67/80: 0.41875
- Absolute value of 67/80: 0.8375
Trigonometric Functions
- Sine of 67/80: 0.7429721376359
- Cosine of 67/80: 0.66932234588182
- Tangent of 67/80: 1.1100363557369
Exponential and Logarithmic Functions
- e^67/80: 2.3105832919575
- Natural log of 67/80: -0.17733401528292
Floor and Ceiling Functions
- Floor of 67/80: 0
- Ceiling of 67/80: 1
Interesting Properties and Relationships
- The sum of 67/80 and its additive inverse (-67/80) is always 0.
- The product of 67/80 and its additive inverse is: -4489
- The average of 67/80 and its additive inverse is always 0.
- The distance between 67/80 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/80 = 0
The solution to this equation is x = -67/80, which is the additive inverse of 67/80.
Graphical Representation
On a coordinate plane:
- The point (67/80, 0) is reflected across the y-axis to (-67/80, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/80 and Its Additive Inverse
Consider the alternating series: 67/80 + (-67/80) + 67/80 + (-67/80) + ...
The sum of this series oscillates between 0 and 67/80, never converging unless 67/80 is 0.
In Number Theory
For integer values:
- If 67/80 is even, its additive inverse is also even.
- If 67/80 is odd, its additive inverse is also odd.
- The sum of the digits of 67/80 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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