9/20 Additive Inverse :
The additive inverse of 9/20 is -9/20.
This means that when we add 9/20 and -9/20, the result is zero:
9/20 + (-9/20) = 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: 9/20
- Additive inverse: -9/20
To verify: 9/20 + (-9/20) = 0
Extended Mathematical Exploration of 9/20
Let's explore various mathematical operations and concepts related to 9/20 and its additive inverse -9/20.
Basic Operations and Properties
- Square of 9/20: 0.2025
- Cube of 9/20: 0.091125
- Square root of |9/20|: 0.67082039324994
- Reciprocal of 9/20: 2.2222222222222
- Double of 9/20: 0.9
- Half of 9/20: 0.225
- Absolute value of 9/20: 0.45
Trigonometric Functions
- Sine of 9/20: 0.43496553411123
- Cosine of 9/20: 0.90044710235268
- Tangent of 9/20: 0.48305506561658
Exponential and Logarithmic Functions
- e^9/20: 1.5683121854902
- Natural log of 9/20: -0.79850769621777
Floor and Ceiling Functions
- Floor of 9/20: 0
- Ceiling of 9/20: 1
Interesting Properties and Relationships
- The sum of 9/20 and its additive inverse (-9/20) is always 0.
- The product of 9/20 and its additive inverse is: -81
- The average of 9/20 and its additive inverse is always 0.
- The distance between 9/20 and its additive inverse on a number line is: 18
Applications in Algebra
Consider the equation: x + 9/20 = 0
The solution to this equation is x = -9/20, which is the additive inverse of 9/20.
Graphical Representation
On a coordinate plane:
- The point (9/20, 0) is reflected across the y-axis to (-9/20, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 9/20 and Its Additive Inverse
Consider the alternating series: 9/20 + (-9/20) + 9/20 + (-9/20) + ...
The sum of this series oscillates between 0 and 9/20, never converging unless 9/20 is 0.
In Number Theory
For integer values:
- If 9/20 is even, its additive inverse is also even.
- If 9/20 is odd, its additive inverse is also odd.
- The sum of the digits of 9/20 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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