12/20 Additive Inverse :
The additive inverse of 12/20 is -12/20.
This means that when we add 12/20 and -12/20, the result is zero:
12/20 + (-12/20) = 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: 12/20
- Additive inverse: -12/20
To verify: 12/20 + (-12/20) = 0
Extended Mathematical Exploration of 12/20
Let's explore various mathematical operations and concepts related to 12/20 and its additive inverse -12/20.
Basic Operations and Properties
- Square of 12/20: 0.36
- Cube of 12/20: 0.216
- Square root of |12/20|: 0.77459666924148
- Reciprocal of 12/20: 1.6666666666667
- Double of 12/20: 1.2
- Half of 12/20: 0.3
- Absolute value of 12/20: 0.6
Trigonometric Functions
- Sine of 12/20: 0.56464247339504
- Cosine of 12/20: 0.82533561490968
- Tangent of 12/20: 0.68413680834169
Exponential and Logarithmic Functions
- e^12/20: 1.8221188003905
- Natural log of 12/20: -0.51082562376599
Floor and Ceiling Functions
- Floor of 12/20: 0
- Ceiling of 12/20: 1
Interesting Properties and Relationships
- The sum of 12/20 and its additive inverse (-12/20) is always 0.
- The product of 12/20 and its additive inverse is: -144
- The average of 12/20 and its additive inverse is always 0.
- The distance between 12/20 and its additive inverse on a number line is: 24
Applications in Algebra
Consider the equation: x + 12/20 = 0
The solution to this equation is x = -12/20, which is the additive inverse of 12/20.
Graphical Representation
On a coordinate plane:
- The point (12/20, 0) is reflected across the y-axis to (-12/20, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 12/20 and Its Additive Inverse
Consider the alternating series: 12/20 + (-12/20) + 12/20 + (-12/20) + ...
The sum of this series oscillates between 0 and 12/20, never converging unless 12/20 is 0.
In Number Theory
For integer values:
- If 12/20 is even, its additive inverse is also even.
- If 12/20 is odd, its additive inverse is also odd.
- The sum of the digits of 12/20 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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