55/65 Additive Inverse :
The additive inverse of 55/65 is -55/65.
This means that when we add 55/65 and -55/65, the result is zero:
55/65 + (-55/65) = 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: 55/65
- Additive inverse: -55/65
To verify: 55/65 + (-55/65) = 0
Extended Mathematical Exploration of 55/65
Let's explore various mathematical operations and concepts related to 55/65 and its additive inverse -55/65.
Basic Operations and Properties
- Square of 55/65: 0.71597633136095
- Cube of 55/65: 0.60582612653619
- Square root of |55/65|: 0.9198662110078
- Reciprocal of 55/65: 1.1818181818182
- Double of 55/65: 1.6923076923077
- Half of 55/65: 0.42307692307692
- Absolute value of 55/65: 0.84615384615385
Trigonometric Functions
- Sine of 55/65: 0.74873645788284
- Cosine of 55/65: 0.66286779725452
- Tangent of 55/65: 1.1295411558443
Exponential and Logarithmic Functions
- e^55/65: 2.3306654931034
- Natural log of 55/65: -0.16705408466317
Floor and Ceiling Functions
- Floor of 55/65: 0
- Ceiling of 55/65: 1
Interesting Properties and Relationships
- The sum of 55/65 and its additive inverse (-55/65) is always 0.
- The product of 55/65 and its additive inverse is: -3025
- The average of 55/65 and its additive inverse is always 0.
- The distance between 55/65 and its additive inverse on a number line is: 110
Applications in Algebra
Consider the equation: x + 55/65 = 0
The solution to this equation is x = -55/65, which is the additive inverse of 55/65.
Graphical Representation
On a coordinate plane:
- The point (55/65, 0) is reflected across the y-axis to (-55/65, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 55/65 and Its Additive Inverse
Consider the alternating series: 55/65 + (-55/65) + 55/65 + (-55/65) + ...
The sum of this series oscillates between 0 and 55/65, never converging unless 55/65 is 0.
In Number Theory
For integer values:
- If 55/65 is even, its additive inverse is also even.
- If 55/65 is odd, its additive inverse is also odd.
- The sum of the digits of 55/65 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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