33/34 Additive Inverse :
The additive inverse of 33/34 is -33/34.
This means that when we add 33/34 and -33/34, the result is zero:
33/34 + (-33/34) = 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: 33/34
- Additive inverse: -33/34
To verify: 33/34 + (-33/34) = 0
Extended Mathematical Exploration of 33/34
Let's explore various mathematical operations and concepts related to 33/34 and its additive inverse -33/34.
Basic Operations and Properties
- Square of 33/34: 0.94204152249135
- Cube of 33/34: 0.91433441888866
- Square root of |33/34|: 0.98518436614378
- Reciprocal of 33/34: 1.030303030303
- Double of 33/34: 1.9411764705882
- Half of 33/34: 0.48529411764706
- Absolute value of 33/34: 0.97058823529412
Trigonometric Functions
- Sine of 33/34: 0.82521809974146
- Cosine of 33/34: 0.56481420649545
- Tangent of 33/34: 1.461043455089
Exponential and Logarithmic Functions
- e^33/34: 2.6394966478703
- Natural log of 33/34: -0.029852963149681
Floor and Ceiling Functions
- Floor of 33/34: 0
- Ceiling of 33/34: 1
Interesting Properties and Relationships
- The sum of 33/34 and its additive inverse (-33/34) is always 0.
- The product of 33/34 and its additive inverse is: -1089
- The average of 33/34 and its additive inverse is always 0.
- The distance between 33/34 and its additive inverse on a number line is: 66
Applications in Algebra
Consider the equation: x + 33/34 = 0
The solution to this equation is x = -33/34, which is the additive inverse of 33/34.
Graphical Representation
On a coordinate plane:
- The point (33/34, 0) is reflected across the y-axis to (-33/34, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 33/34 and Its Additive Inverse
Consider the alternating series: 33/34 + (-33/34) + 33/34 + (-33/34) + ...
The sum of this series oscillates between 0 and 33/34, never converging unless 33/34 is 0.
In Number Theory
For integer values:
- If 33/34 is even, its additive inverse is also even.
- If 33/34 is odd, its additive inverse is also odd.
- The sum of the digits of 33/34 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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