18/21 Additive Inverse :
The additive inverse of 18/21 is -18/21.
This means that when we add 18/21 and -18/21, the result is zero:
18/21 + (-18/21) = 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: 18/21
- Additive inverse: -18/21
To verify: 18/21 + (-18/21) = 0
Extended Mathematical Exploration of 18/21
Let's explore various mathematical operations and concepts related to 18/21 and its additive inverse -18/21.
Basic Operations and Properties
- Square of 18/21: 0.73469387755102
- Cube of 18/21: 0.62973760932945
- Square root of |18/21|: 0.92582009977255
- Reciprocal of 18/21: 1.1666666666667
- Double of 18/21: 1.7142857142857
- Half of 18/21: 0.42857142857143
- Absolute value of 18/21: 0.85714285714286
Trigonometric Functions
- Sine of 18/21: 0.75597536514673
- Cosine of 18/21: 0.65460006667527
- Tangent of 18/21: 1.1548660069443
Exponential and Logarithmic Functions
- e^18/21: 2.3564184423837
- Natural log of 18/21: -0.15415067982726
Floor and Ceiling Functions
- Floor of 18/21: 0
- Ceiling of 18/21: 1
Interesting Properties and Relationships
- The sum of 18/21 and its additive inverse (-18/21) is always 0.
- The product of 18/21 and its additive inverse is: -324
- The average of 18/21 and its additive inverse is always 0.
- The distance between 18/21 and its additive inverse on a number line is: 36
Applications in Algebra
Consider the equation: x + 18/21 = 0
The solution to this equation is x = -18/21, which is the additive inverse of 18/21.
Graphical Representation
On a coordinate plane:
- The point (18/21, 0) is reflected across the y-axis to (-18/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 18/21 and Its Additive Inverse
Consider the alternating series: 18/21 + (-18/21) + 18/21 + (-18/21) + ...
The sum of this series oscillates between 0 and 18/21, never converging unless 18/21 is 0.
In Number Theory
For integer values:
- If 18/21 is even, its additive inverse is also even.
- If 18/21 is odd, its additive inverse is also odd.
- The sum of the digits of 18/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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