80/90 Additive Inverse :
The additive inverse of 80/90 is -80/90.
This means that when we add 80/90 and -80/90, the result is zero:
80/90 + (-80/90) = 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: 80/90
- Additive inverse: -80/90
To verify: 80/90 + (-80/90) = 0
Extended Mathematical Exploration of 80/90
Let's explore various mathematical operations and concepts related to 80/90 and its additive inverse -80/90.
Basic Operations and Properties
- Square of 80/90: 0.79012345679012
- Cube of 80/90: 0.70233196159122
- Square root of |80/90|: 0.94280904158206
- Reciprocal of 80/90: 1.125
- Double of 80/90: 1.7777777777778
- Half of 80/90: 0.44444444444444
- Absolute value of 80/90: 0.88888888888889
Trigonometric Functions
- Sine of 80/90: 0.77637192130066
- Cosine of 80/90: 0.63027505092295
- Tangent of 80/90: 1.2317985935883
Exponential and Logarithmic Functions
- e^80/90: 2.4324254542872
- Natural log of 80/90: -0.11778303565638
Floor and Ceiling Functions
- Floor of 80/90: 0
- Ceiling of 80/90: 1
Interesting Properties and Relationships
- The sum of 80/90 and its additive inverse (-80/90) is always 0.
- The product of 80/90 and its additive inverse is: -6400
- The average of 80/90 and its additive inverse is always 0.
- The distance between 80/90 and its additive inverse on a number line is: 160
Applications in Algebra
Consider the equation: x + 80/90 = 0
The solution to this equation is x = -80/90, which is the additive inverse of 80/90.
Graphical Representation
On a coordinate plane:
- The point (80/90, 0) is reflected across the y-axis to (-80/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 80/90 and Its Additive Inverse
Consider the alternating series: 80/90 + (-80/90) + 80/90 + (-80/90) + ...
The sum of this series oscillates between 0 and 80/90, never converging unless 80/90 is 0.
In Number Theory
For integer values:
- If 80/90 is even, its additive inverse is also even.
- If 80/90 is odd, its additive inverse is also odd.
- The sum of the digits of 80/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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