8/21 Additive Inverse :
The additive inverse of 8/21 is -8/21.
This means that when we add 8/21 and -8/21, the result is zero:
8/21 + (-8/21) = 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: 8/21
- Additive inverse: -8/21
To verify: 8/21 + (-8/21) = 0
Extended Mathematical Exploration of 8/21
Let's explore various mathematical operations and concepts related to 8/21 and its additive inverse -8/21.
Basic Operations and Properties
- Square of 8/21: 0.14512471655329
- Cube of 8/21: 0.055285606306014
- Square root of |8/21|: 0.61721339984837
- Reciprocal of 8/21: 2.625
- Double of 8/21: 0.76190476190476
- Half of 8/21: 0.19047619047619
- Absolute value of 8/21: 0.38095238095238
Trigonometric Functions
- Sine of 8/21: 0.37180474357147
- Cosine of 8/21: 0.92831095687693
- Tangent of 8/21: 0.40051745680382
Exponential and Logarithmic Functions
- e^8/21: 1.4636779048024
- Natural log of 8/21: -0.96508089604359
Floor and Ceiling Functions
- Floor of 8/21: 0
- Ceiling of 8/21: 1
Interesting Properties and Relationships
- The sum of 8/21 and its additive inverse (-8/21) is always 0.
- The product of 8/21 and its additive inverse is: -64
- The average of 8/21 and its additive inverse is always 0.
- The distance between 8/21 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8/21 = 0
The solution to this equation is x = -8/21, which is the additive inverse of 8/21.
Graphical Representation
On a coordinate plane:
- The point (8/21, 0) is reflected across the y-axis to (-8/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8/21 and Its Additive Inverse
Consider the alternating series: 8/21 + (-8/21) + 8/21 + (-8/21) + ...
The sum of this series oscillates between 0 and 8/21, never converging unless 8/21 is 0.
In Number Theory
For integer values:
- If 8/21 is even, its additive inverse is also even.
- If 8/21 is odd, its additive inverse is also odd.
- The sum of the digits of 8/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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