84/85 Additive Inverse :
The additive inverse of 84/85 is -84/85.
This means that when we add 84/85 and -84/85, the result is zero:
84/85 + (-84/85) = 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: 84/85
- Additive inverse: -84/85
To verify: 84/85 + (-84/85) = 0
Extended Mathematical Exploration of 84/85
Let's explore various mathematical operations and concepts related to 84/85 and its additive inverse -84/85.
Basic Operations and Properties
- Square of 84/85: 0.97660899653979
- Cube of 84/85: 0.96511947893344
- Square root of |84/85|: 0.99410024349542
- Reciprocal of 84/85: 1.0119047619048
- Double of 84/85: 1.9764705882353
- Half of 84/85: 0.49411764705882
- Absolute value of 84/85: 0.98823529411765
Trigonometric Functions
- Sine of 84/85: 0.83505640110831
- Cosine of 84/85: 0.55016434541692
- Tangent of 84/85: 1.5178308228526
Exponential and Logarithmic Functions
- e^84/85: 2.6864894230847
- Natural log of 84/85: -0.011834457647003
Floor and Ceiling Functions
- Floor of 84/85: 0
- Ceiling of 84/85: 1
Interesting Properties and Relationships
- The sum of 84/85 and its additive inverse (-84/85) is always 0.
- The product of 84/85 and its additive inverse is: -7056
- The average of 84/85 and its additive inverse is always 0.
- The distance between 84/85 and its additive inverse on a number line is: 168
Applications in Algebra
Consider the equation: x + 84/85 = 0
The solution to this equation is x = -84/85, which is the additive inverse of 84/85.
Graphical Representation
On a coordinate plane:
- The point (84/85, 0) is reflected across the y-axis to (-84/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 84/85 and Its Additive Inverse
Consider the alternating series: 84/85 + (-84/85) + 84/85 + (-84/85) + ...
The sum of this series oscillates between 0 and 84/85, never converging unless 84/85 is 0.
In Number Theory
For integer values:
- If 84/85 is even, its additive inverse is also even.
- If 84/85 is odd, its additive inverse is also odd.
- The sum of the digits of 84/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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