80/87 Additive Inverse :
The additive inverse of 80/87 is -80/87.
This means that when we add 80/87 and -80/87, the result is zero:
80/87 + (-80/87) = 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: 80/87
- Additive inverse: -80/87
To verify: 80/87 + (-80/87) = 0
Extended Mathematical Exploration of 80/87
Let's explore various mathematical operations and concepts related to 80/87 and its additive inverse -80/87.
Basic Operations and Properties
- Square of 80/87: 0.84555423437706
- Cube of 80/87: 0.77752113505937
- Square root of |80/87|: 0.95892660297077
- Reciprocal of 80/87: 1.0875
- Double of 80/87: 1.8390804597701
- Half of 80/87: 0.45977011494253
- Absolute value of 80/87: 0.91954022988506
Trigonometric Functions
- Sine of 80/87: 0.79532299795259
- Cosine of 80/87: 0.60618588644714
- Tangent of 80/87: 1.3120117372148
Exponential and Logarithmic Functions
- e^80/87: 2.5081369583823
- Natural log of 80/87: -0.083881483980702
Floor and Ceiling Functions
- Floor of 80/87: 0
- Ceiling of 80/87: 1
Interesting Properties and Relationships
- The sum of 80/87 and its additive inverse (-80/87) is always 0.
- The product of 80/87 and its additive inverse is: -6400
- The average of 80/87 and its additive inverse is always 0.
- The distance between 80/87 and its additive inverse on a number line is: 160
Applications in Algebra
Consider the equation: x + 80/87 = 0
The solution to this equation is x = -80/87, which is the additive inverse of 80/87.
Graphical Representation
On a coordinate plane:
- The point (80/87, 0) is reflected across the y-axis to (-80/87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 80/87 and Its Additive Inverse
Consider the alternating series: 80/87 + (-80/87) + 80/87 + (-80/87) + ...
The sum of this series oscillates between 0 and 80/87, never converging unless 80/87 is 0.
In Number Theory
For integer values:
- If 80/87 is even, its additive inverse is also even.
- If 80/87 is odd, its additive inverse is also odd.
- The sum of the digits of 80/87 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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