68/72 Additive Inverse :
The additive inverse of 68/72 is -68/72.
This means that when we add 68/72 and -68/72, the result is zero:
68/72 + (-68/72) = 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: 68/72
- Additive inverse: -68/72
To verify: 68/72 + (-68/72) = 0
Extended Mathematical Exploration of 68/72
Let's explore various mathematical operations and concepts related to 68/72 and its additive inverse -68/72.
Basic Operations and Properties
- Square of 68/72: 0.89197530864198
- Cube of 68/72: 0.84242112482853
- Square root of |68/72|: 0.97182531580755
- Reciprocal of 68/72: 1.0588235294118
- Double of 68/72: 1.8888888888889
- Half of 68/72: 0.47222222222222
- Absolute value of 68/72: 0.94444444444444
Trigonometric Functions
- Sine of 68/72: 0.8101713960173
- Cosine of 68/72: 0.58619306467697
- Tangent of 68/72: 1.3820896984917
Exponential and Logarithmic Functions
- e^68/72: 2.571384434788
- Natural log of 68/72: -0.057158413839949
Floor and Ceiling Functions
- Floor of 68/72: 0
- Ceiling of 68/72: 1
Interesting Properties and Relationships
- The sum of 68/72 and its additive inverse (-68/72) is always 0.
- The product of 68/72 and its additive inverse is: -4624
- The average of 68/72 and its additive inverse is always 0.
- The distance between 68/72 and its additive inverse on a number line is: 136
Applications in Algebra
Consider the equation: x + 68/72 = 0
The solution to this equation is x = -68/72, which is the additive inverse of 68/72.
Graphical Representation
On a coordinate plane:
- The point (68/72, 0) is reflected across the y-axis to (-68/72, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 68/72 and Its Additive Inverse
Consider the alternating series: 68/72 + (-68/72) + 68/72 + (-68/72) + ...
The sum of this series oscillates between 0 and 68/72, never converging unless 68/72 is 0.
In Number Theory
For integer values:
- If 68/72 is even, its additive inverse is also even.
- If 68/72 is odd, its additive inverse is also odd.
- The sum of the digits of 68/72 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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