21/33 Additive Inverse :
The additive inverse of 21/33 is -21/33.
This means that when we add 21/33 and -21/33, the result is zero:
21/33 + (-21/33) = 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: 21/33
- Additive inverse: -21/33
To verify: 21/33 + (-21/33) = 0
Extended Mathematical Exploration of 21/33
Let's explore various mathematical operations and concepts related to 21/33 and its additive inverse -21/33.
Basic Operations and Properties
- Square of 21/33: 0.40495867768595
- Cube of 21/33: 0.25770097670924
- Square root of |21/33|: 0.79772403521747
- Reciprocal of 21/33: 1.5714285714286
- Double of 21/33: 1.2727272727273
- Half of 21/33: 0.31818181818182
- Absolute value of 21/33: 0.63636363636364
Trigonometric Functions
- Sine of 21/33: 0.59427478754829
- Cosine of 21/33: 0.80426206977852
- Tangent of 21/33: 0.73890689351039
Exponential and Logarithmic Functions
- e^21/33: 1.8895971087303
- Natural log of 21/33: -0.45198512374306
Floor and Ceiling Functions
- Floor of 21/33: 0
- Ceiling of 21/33: 1
Interesting Properties and Relationships
- The sum of 21/33 and its additive inverse (-21/33) is always 0.
- The product of 21/33 and its additive inverse is: -441
- The average of 21/33 and its additive inverse is always 0.
- The distance between 21/33 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/33 = 0
The solution to this equation is x = -21/33, which is the additive inverse of 21/33.
Graphical Representation
On a coordinate plane:
- The point (21/33, 0) is reflected across the y-axis to (-21/33, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/33 and Its Additive Inverse
Consider the alternating series: 21/33 + (-21/33) + 21/33 + (-21/33) + ...
The sum of this series oscillates between 0 and 21/33, never converging unless 21/33 is 0.
In Number Theory
For integer values:
- If 21/33 is even, its additive inverse is also even.
- If 21/33 is odd, its additive inverse is also odd.
- The sum of the digits of 21/33 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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