72/73 Additive Inverse :
The additive inverse of 72/73 is -72/73.
This means that when we add 72/73 and -72/73, the result is zero:
72/73 + (-72/73) = 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: 72/73
- Additive inverse: -72/73
To verify: 72/73 + (-72/73) = 0
Extended Mathematical Exploration of 72/73
Let's explore various mathematical operations and concepts related to 72/73 and its additive inverse -72/73.
Basic Operations and Properties
- Square of 72/73: 0.97279039219366
- Cube of 72/73: 0.95946449641018
- Square root of |72/73|: 0.99312706632284
- Reciprocal of 72/73: 1.0138888888889
- Double of 72/73: 1.972602739726
- Half of 72/73: 0.49315068493151
- Absolute value of 72/73: 0.98630136986301
Trigonometric Functions
- Sine of 72/73: 0.8339908640186
- Cosine of 72/73: 0.55177825141401
- Tangent of 72/73: 1.511460195978
Exponential and Logarithmic Functions
- e^72/73: 2.6812989766125
- Natural log of 72/73: -0.013793322132336
Floor and Ceiling Functions
- Floor of 72/73: 0
- Ceiling of 72/73: 1
Interesting Properties and Relationships
- The sum of 72/73 and its additive inverse (-72/73) is always 0.
- The product of 72/73 and its additive inverse is: -5184
- The average of 72/73 and its additive inverse is always 0.
- The distance between 72/73 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72/73 = 0
The solution to this equation is x = -72/73, which is the additive inverse of 72/73.
Graphical Representation
On a coordinate plane:
- The point (72/73, 0) is reflected across the y-axis to (-72/73, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72/73 and Its Additive Inverse
Consider the alternating series: 72/73 + (-72/73) + 72/73 + (-72/73) + ...
The sum of this series oscillates between 0 and 72/73, never converging unless 72/73 is 0.
In Number Theory
For integer values:
- If 72/73 is even, its additive inverse is also even.
- If 72/73 is odd, its additive inverse is also odd.
- The sum of the digits of 72/73 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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