84/89 Additive Inverse :
The additive inverse of 84/89 is -84/89.
This means that when we add 84/89 and -84/89, the result is zero:
84/89 + (-84/89) = 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: 84/89
- Additive inverse: -84/89
To verify: 84/89 + (-84/89) = 0
Extended Mathematical Exploration of 84/89
Let's explore various mathematical operations and concepts related to 84/89 and its additive inverse -84/89.
Basic Operations and Properties
- Square of 84/89: 0.89079661658881
- Cube of 84/89: 0.84075186284787
- Square root of |84/89|: 0.97150410432437
- Reciprocal of 84/89: 1.0595238095238
- Double of 84/89: 1.8876404494382
- Half of 84/89: 0.47191011235955
- Absolute value of 84/89: 0.9438202247191
Trigonometric Functions
- Sine of 84/89: 0.80980532492549
- Cosine of 84/89: 0.58669867540529
- Tangent of 84/89: 1.380274677399
Exponential and Logarithmic Functions
- e^84/89: 2.5697798267685
- Natural log of 84/89: -0.057819570888826
Floor and Ceiling Functions
- Floor of 84/89: 0
- Ceiling of 84/89: 1
Interesting Properties and Relationships
- The sum of 84/89 and its additive inverse (-84/89) is always 0.
- The product of 84/89 and its additive inverse is: -7056
- The average of 84/89 and its additive inverse is always 0.
- The distance between 84/89 and its additive inverse on a number line is: 168
Applications in Algebra
Consider the equation: x + 84/89 = 0
The solution to this equation is x = -84/89, which is the additive inverse of 84/89.
Graphical Representation
On a coordinate plane:
- The point (84/89, 0) is reflected across the y-axis to (-84/89, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 84/89 and Its Additive Inverse
Consider the alternating series: 84/89 + (-84/89) + 84/89 + (-84/89) + ...
The sum of this series oscillates between 0 and 84/89, never converging unless 84/89 is 0.
In Number Theory
For integer values:
- If 84/89 is even, its additive inverse is also even.
- If 84/89 is odd, its additive inverse is also odd.
- The sum of the digits of 84/89 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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