2/9 Additive Inverse :
The additive inverse of 2/9 is -2/9.
This means that when we add 2/9 and -2/9, the result is zero:
2/9 + (-2/9) = 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: 2/9
- Additive inverse: -2/9
To verify: 2/9 + (-2/9) = 0
Extended Mathematical Exploration of 2/9
Let's explore various mathematical operations and concepts related to 2/9 and its additive inverse -2/9.
Basic Operations and Properties
- Square of 2/9: 0.049382716049383
- Cube of 2/9: 0.010973936899863
- Square root of |2/9|: 0.47140452079103
- Reciprocal of 2/9: 4.5
- Double of 2/9: 0.44444444444444
- Half of 2/9: 0.11111111111111
- Absolute value of 2/9: 0.22222222222222
Trigonometric Functions
- Sine of 2/9: 0.22039774345612
- Cosine of 2/9: 0.97541008538945
- Tangent of 2/9: 0.22595393133353
Exponential and Logarithmic Functions
- e^2/9: 1.2488488690017
- Natural log of 2/9: -1.5040773967763
Floor and Ceiling Functions
- Floor of 2/9: 0
- Ceiling of 2/9: 1
Interesting Properties and Relationships
- The sum of 2/9 and its additive inverse (-2/9) is always 0.
- The product of 2/9 and its additive inverse is: -4
- The average of 2/9 and its additive inverse is always 0.
- The distance between 2/9 and its additive inverse on a number line is: 4
Applications in Algebra
Consider the equation: x + 2/9 = 0
The solution to this equation is x = -2/9, which is the additive inverse of 2/9.
Graphical Representation
On a coordinate plane:
- The point (2/9, 0) is reflected across the y-axis to (-2/9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 2/9 and Its Additive Inverse
Consider the alternating series: 2/9 + (-2/9) + 2/9 + (-2/9) + ...
The sum of this series oscillates between 0 and 2/9, never converging unless 2/9 is 0.
In Number Theory
For integer values:
- If 2/9 is even, its additive inverse is also even.
- If 2/9 is odd, its additive inverse is also odd.
- The sum of the digits of 2/9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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