55/67 Additive Inverse :
The additive inverse of 55/67 is -55/67.
This means that when we add 55/67 and -55/67, the result is zero:
55/67 + (-55/67) = 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: 55/67
- Additive inverse: -55/67
To verify: 55/67 + (-55/67) = 0
Extended Mathematical Exploration of 55/67
Let's explore various mathematical operations and concepts related to 55/67 and its additive inverse -55/67.
Basic Operations and Properties
- Square of 55/67: 0.67386945867677
- Cube of 55/67: 0.55317642130182
- Square root of |55/67|: 0.90603284840455
- Reciprocal of 55/67: 1.2181818181818
- Double of 55/67: 1.6417910447761
- Half of 55/67: 0.41044776119403
- Absolute value of 55/67: 0.82089552238806
Trigonometric Functions
- Sine of 55/67: 0.73175648083501
- Cosine of 55/67: 0.68156617635851
- Tangent of 55/67: 1.0736396643752
Exponential and Logarithmic Functions
- e^55/67: 2.2725340316663
- Natural log of 55/67: -0.1973594341585
Floor and Ceiling Functions
- Floor of 55/67: 0
- Ceiling of 55/67: 1
Interesting Properties and Relationships
- The sum of 55/67 and its additive inverse (-55/67) is always 0.
- The product of 55/67 and its additive inverse is: -3025
- The average of 55/67 and its additive inverse is always 0.
- The distance between 55/67 and its additive inverse on a number line is: 110
Applications in Algebra
Consider the equation: x + 55/67 = 0
The solution to this equation is x = -55/67, which is the additive inverse of 55/67.
Graphical Representation
On a coordinate plane:
- The point (55/67, 0) is reflected across the y-axis to (-55/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 55/67 and Its Additive Inverse
Consider the alternating series: 55/67 + (-55/67) + 55/67 + (-55/67) + ...
The sum of this series oscillates between 0 and 55/67, never converging unless 55/67 is 0.
In Number Theory
For integer values:
- If 55/67 is even, its additive inverse is also even.
- If 55/67 is odd, its additive inverse is also odd.
- The sum of the digits of 55/67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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