33/45 Additive Inverse :
The additive inverse of 33/45 is -33/45.
This means that when we add 33/45 and -33/45, the result is zero:
33/45 + (-33/45) = 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: 33/45
- Additive inverse: -33/45
To verify: 33/45 + (-33/45) = 0
Extended Mathematical Exploration of 33/45
Let's explore various mathematical operations and concepts related to 33/45 and its additive inverse -33/45.
Basic Operations and Properties
- Square of 33/45: 0.53777777777778
- Cube of 33/45: 0.39437037037037
- Square root of |33/45|: 0.85634883857768
- Reciprocal of 33/45: 1.3636363636364
- Double of 33/45: 1.4666666666667
- Half of 33/45: 0.36666666666667
- Absolute value of 33/45: 0.73333333333333
Trigonometric Functions
- Sine of 33/45: 0.66934984025047
- Cosine of 33/45: 0.74294736782404
- Tangent of 33/45: 0.9009384368786
Exponential and Logarithmic Functions
- e^33/45: 2.0820090840785
- Natural log of 33/45: -0.31015492830384
Floor and Ceiling Functions
- Floor of 33/45: 0
- Ceiling of 33/45: 1
Interesting Properties and Relationships
- The sum of 33/45 and its additive inverse (-33/45) is always 0.
- The product of 33/45 and its additive inverse is: -1089
- The average of 33/45 and its additive inverse is always 0.
- The distance between 33/45 and its additive inverse on a number line is: 66
Applications in Algebra
Consider the equation: x + 33/45 = 0
The solution to this equation is x = -33/45, which is the additive inverse of 33/45.
Graphical Representation
On a coordinate plane:
- The point (33/45, 0) is reflected across the y-axis to (-33/45, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 33/45 and Its Additive Inverse
Consider the alternating series: 33/45 + (-33/45) + 33/45 + (-33/45) + ...
The sum of this series oscillates between 0 and 33/45, never converging unless 33/45 is 0.
In Number Theory
For integer values:
- If 33/45 is even, its additive inverse is also even.
- If 33/45 is odd, its additive inverse is also odd.
- The sum of the digits of 33/45 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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