84/99 Additive Inverse :
The additive inverse of 84/99 is -84/99.
This means that when we add 84/99 and -84/99, the result is zero:
84/99 + (-84/99) = 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: 84/99
- Additive inverse: -84/99
To verify: 84/99 + (-84/99) = 0
Extended Mathematical Exploration of 84/99
Let's explore various mathematical operations and concepts related to 84/99 and its additive inverse -84/99.
Basic Operations and Properties
- Square of 84/99: 0.71992653810836
- Cube of 84/99: 0.61084675960709
- Square root of |84/99|: 0.92113237294368
- Reciprocal of 84/99: 1.1785714285714
- Double of 84/99: 1.6969696969697
- Half of 84/99: 0.42424242424242
- Absolute value of 84/99: 0.84848484848485
Trigonometric Functions
- Sine of 84/99: 0.75027956870835
- Cosine of 84/99: 0.66112069153734
- Tangent of 84/99: 1.134860212836
Exponential and Logarithmic Functions
- e^84/99: 2.3361046166426
- Natural log of 84/99: -0.16430305129128
Floor and Ceiling Functions
- Floor of 84/99: 0
- Ceiling of 84/99: 1
Interesting Properties and Relationships
- The sum of 84/99 and its additive inverse (-84/99) is always 0.
- The product of 84/99 and its additive inverse is: -7056
- The average of 84/99 and its additive inverse is always 0.
- The distance between 84/99 and its additive inverse on a number line is: 168
Applications in Algebra
Consider the equation: x + 84/99 = 0
The solution to this equation is x = -84/99, which is the additive inverse of 84/99.
Graphical Representation
On a coordinate plane:
- The point (84/99, 0) is reflected across the y-axis to (-84/99, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 84/99 and Its Additive Inverse
Consider the alternating series: 84/99 + (-84/99) + 84/99 + (-84/99) + ...
The sum of this series oscillates between 0 and 84/99, never converging unless 84/99 is 0.
In Number Theory
For integer values:
- If 84/99 is even, its additive inverse is also even.
- If 84/99 is odd, its additive inverse is also odd.
- The sum of the digits of 84/99 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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