55/69 Additive Inverse :
The additive inverse of 55/69 is -55/69.
This means that when we add 55/69 and -55/69, the result is zero:
55/69 + (-55/69) = 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: 55/69
- Additive inverse: -55/69
To verify: 55/69 + (-55/69) = 0
Extended Mathematical Exploration of 55/69
Let's explore various mathematical operations and concepts related to 55/69 and its additive inverse -55/69.
Basic Operations and Properties
- Square of 55/69: 0.63537072043688
- Cube of 55/69: 0.50645492208737
- Square root of |55/69|: 0.8928053815224
- Reciprocal of 55/69: 1.2545454545455
- Double of 55/69: 1.5942028985507
- Half of 55/69: 0.39855072463768
- Absolute value of 55/69: 0.79710144927536
Trigonometric Functions
- Sine of 55/69: 0.71533364052401
- Cosine of 55/69: 0.6987830727305
- Tangent of 55/69: 1.023684843608
Exponential and Logarithmic Functions
- e^55/69: 2.2190994252433
- Natural log of 55/69: -0.22677331936479
Floor and Ceiling Functions
- Floor of 55/69: 0
- Ceiling of 55/69: 1
Interesting Properties and Relationships
- The sum of 55/69 and its additive inverse (-55/69) is always 0.
- The product of 55/69 and its additive inverse is: -3025
- The average of 55/69 and its additive inverse is always 0.
- The distance between 55/69 and its additive inverse on a number line is: 110
Applications in Algebra
Consider the equation: x + 55/69 = 0
The solution to this equation is x = -55/69, which is the additive inverse of 55/69.
Graphical Representation
On a coordinate plane:
- The point (55/69, 0) is reflected across the y-axis to (-55/69, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 55/69 and Its Additive Inverse
Consider the alternating series: 55/69 + (-55/69) + 55/69 + (-55/69) + ...
The sum of this series oscillates between 0 and 55/69, never converging unless 55/69 is 0.
In Number Theory
For integer values:
- If 55/69 is even, its additive inverse is also even.
- If 55/69 is odd, its additive inverse is also odd.
- The sum of the digits of 55/69 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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