12/21 Additive Inverse :
The additive inverse of 12/21 is -12/21.
This means that when we add 12/21 and -12/21, the result is zero:
12/21 + (-12/21) = 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: 12/21
- Additive inverse: -12/21
To verify: 12/21 + (-12/21) = 0
Extended Mathematical Exploration of 12/21
Let's explore various mathematical operations and concepts related to 12/21 and its additive inverse -12/21.
Basic Operations and Properties
- Square of 12/21: 0.3265306122449
- Cube of 12/21: 0.1865889212828
- Square root of |12/21|: 0.75592894601845
- Reciprocal of 12/21: 1.75
- Double of 12/21: 1.1428571428571
- Half of 12/21: 0.28571428571429
- Absolute value of 12/21: 0.57142857142857
Trigonometric Functions
- Sine of 12/21: 0.54083421335883
- Cosine of 12/21: 0.84112921341524
- Tangent of 12/21: 0.64298588698743
Exponential and Logarithmic Functions
- e^12/21: 1.7707949524352
- Natural log of 12/21: -0.55961578793542
Floor and Ceiling Functions
- Floor of 12/21: 0
- Ceiling of 12/21: 1
Interesting Properties and Relationships
- The sum of 12/21 and its additive inverse (-12/21) is always 0.
- The product of 12/21 and its additive inverse is: -144
- The average of 12/21 and its additive inverse is always 0.
- The distance between 12/21 and its additive inverse on a number line is: 24
Applications in Algebra
Consider the equation: x + 12/21 = 0
The solution to this equation is x = -12/21, which is the additive inverse of 12/21.
Graphical Representation
On a coordinate plane:
- The point (12/21, 0) is reflected across the y-axis to (-12/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 12/21 and Its Additive Inverse
Consider the alternating series: 12/21 + (-12/21) + 12/21 + (-12/21) + ...
The sum of this series oscillates between 0 and 12/21, never converging unless 12/21 is 0.
In Number Theory
For integer values:
- If 12/21 is even, its additive inverse is also even.
- If 12/21 is odd, its additive inverse is also odd.
- The sum of the digits of 12/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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