72/81 Additive Inverse :
The additive inverse of 72/81 is -72/81.
This means that when we add 72/81 and -72/81, the result is zero:
72/81 + (-72/81) = 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: 72/81
- Additive inverse: -72/81
To verify: 72/81 + (-72/81) = 0
Extended Mathematical Exploration of 72/81
Let's explore various mathematical operations and concepts related to 72/81 and its additive inverse -72/81.
Basic Operations and Properties
- Square of 72/81: 0.79012345679012
- Cube of 72/81: 0.70233196159122
- Square root of |72/81|: 0.94280904158206
- Reciprocal of 72/81: 1.125
- Double of 72/81: 1.7777777777778
- Half of 72/81: 0.44444444444444
- Absolute value of 72/81: 0.88888888888889
Trigonometric Functions
- Sine of 72/81: 0.77637192130066
- Cosine of 72/81: 0.63027505092295
- Tangent of 72/81: 1.2317985935883
Exponential and Logarithmic Functions
- e^72/81: 2.4324254542872
- Natural log of 72/81: -0.11778303565638
Floor and Ceiling Functions
- Floor of 72/81: 0
- Ceiling of 72/81: 1
Interesting Properties and Relationships
- The sum of 72/81 and its additive inverse (-72/81) is always 0.
- The product of 72/81 and its additive inverse is: -5184
- The average of 72/81 and its additive inverse is always 0.
- The distance between 72/81 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72/81 = 0
The solution to this equation is x = -72/81, which is the additive inverse of 72/81.
Graphical Representation
On a coordinate plane:
- The point (72/81, 0) is reflected across the y-axis to (-72/81, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72/81 and Its Additive Inverse
Consider the alternating series: 72/81 + (-72/81) + 72/81 + (-72/81) + ...
The sum of this series oscillates between 0 and 72/81, never converging unless 72/81 is 0.
In Number Theory
For integer values:
- If 72/81 is even, its additive inverse is also even.
- If 72/81 is odd, its additive inverse is also odd.
- The sum of the digits of 72/81 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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