85/90 Additive Inverse :
The additive inverse of 85/90 is -85/90.
This means that when we add 85/90 and -85/90, the result is zero:
85/90 + (-85/90) = 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: 85/90
- Additive inverse: -85/90
To verify: 85/90 + (-85/90) = 0
Extended Mathematical Exploration of 85/90
Let's explore various mathematical operations and concepts related to 85/90 and its additive inverse -85/90.
Basic Operations and Properties
- Square of 85/90: 0.89197530864198
- Cube of 85/90: 0.84242112482853
- Square root of |85/90|: 0.97182531580755
- Reciprocal of 85/90: 1.0588235294118
- Double of 85/90: 1.8888888888889
- Half of 85/90: 0.47222222222222
- Absolute value of 85/90: 0.94444444444444
Trigonometric Functions
- Sine of 85/90: 0.8101713960173
- Cosine of 85/90: 0.58619306467697
- Tangent of 85/90: 1.3820896984917
Exponential and Logarithmic Functions
- e^85/90: 2.571384434788
- Natural log of 85/90: -0.057158413839949
Floor and Ceiling Functions
- Floor of 85/90: 0
- Ceiling of 85/90: 1
Interesting Properties and Relationships
- The sum of 85/90 and its additive inverse (-85/90) is always 0.
- The product of 85/90 and its additive inverse is: -7225
- The average of 85/90 and its additive inverse is always 0.
- The distance between 85/90 and its additive inverse on a number line is: 170
Applications in Algebra
Consider the equation: x + 85/90 = 0
The solution to this equation is x = -85/90, which is the additive inverse of 85/90.
Graphical Representation
On a coordinate plane:
- The point (85/90, 0) is reflected across the y-axis to (-85/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 85/90 and Its Additive Inverse
Consider the alternating series: 85/90 + (-85/90) + 85/90 + (-85/90) + ...
The sum of this series oscillates between 0 and 85/90, never converging unless 85/90 is 0.
In Number Theory
For integer values:
- If 85/90 is even, its additive inverse is also even.
- If 85/90 is odd, its additive inverse is also odd.
- The sum of the digits of 85/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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