55/66 Additive Inverse :
The additive inverse of 55/66 is -55/66.
This means that when we add 55/66 and -55/66, the result is zero:
55/66 + (-55/66) = 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: 55/66
- Additive inverse: -55/66
To verify: 55/66 + (-55/66) = 0
Extended Mathematical Exploration of 55/66
Let's explore various mathematical operations and concepts related to 55/66 and its additive inverse -55/66.
Basic Operations and Properties
- Square of 55/66: 0.69444444444444
- Cube of 55/66: 0.5787037037037
- Square root of |55/66|: 0.91287092917528
- Reciprocal of 55/66: 1.2
- Double of 55/66: 1.6666666666667
- Half of 55/66: 0.41666666666667
- Absolute value of 55/66: 0.83333333333333
Trigonometric Functions
- Sine of 55/66: 0.74017685319604
- Cosine of 55/66: 0.67241224408306
- Tangent of 55/66: 1.1007783687898
Exponential and Logarithmic Functions
- e^55/66: 2.3009758908928
- Natural log of 55/66: -0.18232155679395
Floor and Ceiling Functions
- Floor of 55/66: 0
- Ceiling of 55/66: 1
Interesting Properties and Relationships
- The sum of 55/66 and its additive inverse (-55/66) is always 0.
- The product of 55/66 and its additive inverse is: -3025
- The average of 55/66 and its additive inverse is always 0.
- The distance between 55/66 and its additive inverse on a number line is: 110
Applications in Algebra
Consider the equation: x + 55/66 = 0
The solution to this equation is x = -55/66, which is the additive inverse of 55/66.
Graphical Representation
On a coordinate plane:
- The point (55/66, 0) is reflected across the y-axis to (-55/66, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 55/66 and Its Additive Inverse
Consider the alternating series: 55/66 + (-55/66) + 55/66 + (-55/66) + ...
The sum of this series oscillates between 0 and 55/66, never converging unless 55/66 is 0.
In Number Theory
For integer values:
- If 55/66 is even, its additive inverse is also even.
- If 55/66 is odd, its additive inverse is also odd.
- The sum of the digits of 55/66 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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