84/97 Additive Inverse :
The additive inverse of 84/97 is -84/97.
This means that when we add 84/97 and -84/97, the result is zero:
84/97 + (-84/97) = 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: 84/97
- Additive inverse: -84/97
To verify: 84/97 + (-84/97) = 0
Extended Mathematical Exploration of 84/97
Let's explore various mathematical operations and concepts related to 84/97 and its additive inverse -84/97.
Basic Operations and Properties
- Square of 84/97: 0.74992028908492
- Cube of 84/97: 0.64941550807354
- Square root of |84/97|: 0.93058013166159
- Reciprocal of 84/97: 1.1547619047619
- Double of 84/97: 1.7319587628866
- Half of 84/97: 0.43298969072165
- Absolute value of 84/97: 0.8659793814433
Trigonometric Functions
- Sine of 84/97: 0.7617301646058
- Cosine of 84/97: 0.64789440214407
- Tangent of 84/97: 1.1757011051261
Exponential and Logarithmic Functions
- e^84/97: 2.3773332622761
- Natural log of 84/97: -0.14389417966007
Floor and Ceiling Functions
- Floor of 84/97: 0
- Ceiling of 84/97: 1
Interesting Properties and Relationships
- The sum of 84/97 and its additive inverse (-84/97) is always 0.
- The product of 84/97 and its additive inverse is: -7056
- The average of 84/97 and its additive inverse is always 0.
- The distance between 84/97 and its additive inverse on a number line is: 168
Applications in Algebra
Consider the equation: x + 84/97 = 0
The solution to this equation is x = -84/97, which is the additive inverse of 84/97.
Graphical Representation
On a coordinate plane:
- The point (84/97, 0) is reflected across the y-axis to (-84/97, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 84/97 and Its Additive Inverse
Consider the alternating series: 84/97 + (-84/97) + 84/97 + (-84/97) + ...
The sum of this series oscillates between 0 and 84/97, never converging unless 84/97 is 0.
In Number Theory
For integer values:
- If 84/97 is even, its additive inverse is also even.
- If 84/97 is odd, its additive inverse is also odd.
- The sum of the digits of 84/97 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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