1/9 Additive Inverse :
The additive inverse of 1/9 is -1/9.
This means that when we add 1/9 and -1/9, the result is zero:
1/9 + (-1/9) = 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: 1/9
- Additive inverse: -1/9
To verify: 1/9 + (-1/9) = 0
Extended Mathematical Exploration of 1/9
Let's explore various mathematical operations and concepts related to 1/9 and its additive inverse -1/9.
Basic Operations and Properties
- Square of 1/9: 0.012345679012346
- Cube of 1/9: 0.0013717421124829
- Square root of |1/9|: 0.33333333333333
- Reciprocal of 1/9: 9
- Double of 1/9: 0.22222222222222
- Half of 1/9: 0.055555555555556
- Absolute value of 1/9: 0.11111111111111
Trigonometric Functions
- Sine of 1/9: 0.11088262850995
- Cosine of 1/9: 0.99383350853889
- Tangent of 1/9: 0.1115706278338
Exponential and Logarithmic Functions
- e^1/9: 1.1175190687419
- Natural log of 1/9: -2.1972245773362
Floor and Ceiling Functions
- Floor of 1/9: 0
- Ceiling of 1/9: 1
Interesting Properties and Relationships
- The sum of 1/9 and its additive inverse (-1/9) is always 0.
- The product of 1/9 and its additive inverse is: -1
- The average of 1/9 and its additive inverse is always 0.
- The distance between 1/9 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/9 = 0
The solution to this equation is x = -1/9, which is the additive inverse of 1/9.
Graphical Representation
On a coordinate plane:
- The point (1/9, 0) is reflected across the y-axis to (-1/9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/9 and Its Additive Inverse
Consider the alternating series: 1/9 + (-1/9) + 1/9 + (-1/9) + ...
The sum of this series oscillates between 0 and 1/9, never converging unless 1/9 is 0.
In Number Theory
For integer values:
- If 1/9 is even, its additive inverse is also even.
- If 1/9 is odd, its additive inverse is also odd.
- The sum of the digits of 1/9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: