21/27 Additive Inverse :
The additive inverse of 21/27 is -21/27.
This means that when we add 21/27 and -21/27, the result is zero:
21/27 + (-21/27) = 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: 21/27
- Additive inverse: -21/27
To verify: 21/27 + (-21/27) = 0
Extended Mathematical Exploration of 21/27
Let's explore various mathematical operations and concepts related to 21/27 and its additive inverse -21/27.
Basic Operations and Properties
- Square of 21/27: 0.60493827160494
- Cube of 21/27: 0.47050754458162
- Square root of |21/27|: 0.8819171036882
- Reciprocal of 21/27: 1.2857142857143
- Double of 21/27: 1.5555555555556
- Half of 21/27: 0.38888888888889
- Absolute value of 21/27: 0.77777777777778
Trigonometric Functions
- Sine of 21/27: 0.70169787614674
- Cosine of 21/27: 0.71247462453842
- Tangent of 21/27: 0.98487420039883
Exponential and Logarithmic Functions
- e^21/27: 2.1766299317162
- Natural log of 21/27: -0.25131442828091
Floor and Ceiling Functions
- Floor of 21/27: 0
- Ceiling of 21/27: 1
Interesting Properties and Relationships
- The sum of 21/27 and its additive inverse (-21/27) is always 0.
- The product of 21/27 and its additive inverse is: -441
- The average of 21/27 and its additive inverse is always 0.
- The distance between 21/27 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/27 = 0
The solution to this equation is x = -21/27, which is the additive inverse of 21/27.
Graphical Representation
On a coordinate plane:
- The point (21/27, 0) is reflected across the y-axis to (-21/27, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/27 and Its Additive Inverse
Consider the alternating series: 21/27 + (-21/27) + 21/27 + (-21/27) + ...
The sum of this series oscillates between 0 and 21/27, never converging unless 21/27 is 0.
In Number Theory
For integer values:
- If 21/27 is even, its additive inverse is also even.
- If 21/27 is odd, its additive inverse is also odd.
- The sum of the digits of 21/27 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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