97/98 Additive Inverse :
The additive inverse of 97/98 is -97/98.
This means that when we add 97/98 and -97/98, the result is zero:
97/98 + (-97/98) = 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: 97/98
- Additive inverse: -97/98
To verify: 97/98 + (-97/98) = 0
Extended Mathematical Exploration of 97/98
Let's explore various mathematical operations and concepts related to 97/98 and its additive inverse -97/98.
Basic Operations and Properties
- Square of 97/98: 0.97969596001666
- Cube of 97/98: 0.96969906246547
- Square root of |97/98|: 0.99488487694172
- Reciprocal of 97/98: 1.0103092783505
- Double of 97/98: 1.9795918367347
- Half of 97/98: 0.49489795918367
- Absolute value of 97/98: 0.98979591836735
Trigonometric Functions
- Sine of 97/98: 0.83591398366878
- Cosine of 97/98: 0.54886046670078
- Tangent of 97/98: 1.5229990760557
Exponential and Logarithmic Functions
- e^97/98: 2.6906852968645
- Natural log of 97/98: -0.010256500167189
Floor and Ceiling Functions
- Floor of 97/98: 0
- Ceiling of 97/98: 1
Interesting Properties and Relationships
- The sum of 97/98 and its additive inverse (-97/98) is always 0.
- The product of 97/98 and its additive inverse is: -9409
- The average of 97/98 and its additive inverse is always 0.
- The distance between 97/98 and its additive inverse on a number line is: 194
Applications in Algebra
Consider the equation: x + 97/98 = 0
The solution to this equation is x = -97/98, which is the additive inverse of 97/98.
Graphical Representation
On a coordinate plane:
- The point (97/98, 0) is reflected across the y-axis to (-97/98, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 97/98 and Its Additive Inverse
Consider the alternating series: 97/98 + (-97/98) + 97/98 + (-97/98) + ...
The sum of this series oscillates between 0 and 97/98, never converging unless 97/98 is 0.
In Number Theory
For integer values:
- If 97/98 is even, its additive inverse is also even.
- If 97/98 is odd, its additive inverse is also odd.
- The sum of the digits of 97/98 and its additive inverse may or may not be the same.
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