68/73 Additive Inverse :
The additive inverse of 68/73 is -68/73.
This means that when we add 68/73 and -68/73, the result is zero:
68/73 + (-68/73) = 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: 68/73
- Additive inverse: -68/73
To verify: 68/73 + (-68/73) = 0
Extended Mathematical Exploration of 68/73
Let's explore various mathematical operations and concepts related to 68/73 and its additive inverse -68/73.
Basic Operations and Properties
- Square of 68/73: 0.86770501032089
- Cube of 68/73: 0.80827316029891
- Square root of |68/73|: 0.96514602486622
- Reciprocal of 68/73: 1.0735294117647
- Double of 68/73: 1.8630136986301
- Half of 68/73: 0.46575342465753
- Absolute value of 68/73: 0.93150684931507
Trigonometric Functions
- Sine of 68/73: 0.80251987619272
- Cosine of 68/73: 0.59662538356629
- Tangent of 68/73: 1.3450984458551
Exponential and Logarithmic Functions
- e^68/73: 2.5383311799038
- Natural log of 68/73: -0.070951735972284
Floor and Ceiling Functions
- Floor of 68/73: 0
- Ceiling of 68/73: 1
Interesting Properties and Relationships
- The sum of 68/73 and its additive inverse (-68/73) is always 0.
- The product of 68/73 and its additive inverse is: -4624
- The average of 68/73 and its additive inverse is always 0.
- The distance between 68/73 and its additive inverse on a number line is: 136
Applications in Algebra
Consider the equation: x + 68/73 = 0
The solution to this equation is x = -68/73, which is the additive inverse of 68/73.
Graphical Representation
On a coordinate plane:
- The point (68/73, 0) is reflected across the y-axis to (-68/73, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 68/73 and Its Additive Inverse
Consider the alternating series: 68/73 + (-68/73) + 68/73 + (-68/73) + ...
The sum of this series oscillates between 0 and 68/73, never converging unless 68/73 is 0.
In Number Theory
For integer values:
- If 68/73 is even, its additive inverse is also even.
- If 68/73 is odd, its additive inverse is also odd.
- The sum of the digits of 68/73 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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