3/9 Additive Inverse :
The additive inverse of 3/9 is -3/9.
This means that when we add 3/9 and -3/9, the result is zero:
3/9 + (-3/9) = 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: 3/9
- Additive inverse: -3/9
To verify: 3/9 + (-3/9) = 0
Extended Mathematical Exploration of 3/9
Let's explore various mathematical operations and concepts related to 3/9 and its additive inverse -3/9.
Basic Operations and Properties
- Square of 3/9: 0.11111111111111
- Cube of 3/9: 0.037037037037037
- Square root of |3/9|: 0.57735026918963
- Reciprocal of 3/9: 3
- Double of 3/9: 0.66666666666667
- Half of 3/9: 0.16666666666667
- Absolute value of 3/9: 0.33333333333333
Trigonometric Functions
- Sine of 3/9: 0.32719469679615
- Cosine of 3/9: 0.94495694631474
- Tangent of 3/9: 0.34625354951058
Exponential and Logarithmic Functions
- e^3/9: 1.3956124250861
- Natural log of 3/9: -1.0986122886681
Floor and Ceiling Functions
- Floor of 3/9: 0
- Ceiling of 3/9: 1
Interesting Properties and Relationships
- The sum of 3/9 and its additive inverse (-3/9) is always 0.
- The product of 3/9 and its additive inverse is: -9
- The average of 3/9 and its additive inverse is always 0.
- The distance between 3/9 and its additive inverse on a number line is: 6
Applications in Algebra
Consider the equation: x + 3/9 = 0
The solution to this equation is x = -3/9, which is the additive inverse of 3/9.
Graphical Representation
On a coordinate plane:
- The point (3/9, 0) is reflected across the y-axis to (-3/9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 3/9 and Its Additive Inverse
Consider the alternating series: 3/9 + (-3/9) + 3/9 + (-3/9) + ...
The sum of this series oscillates between 0 and 3/9, never converging unless 3/9 is 0.
In Number Theory
For integer values:
- If 3/9 is even, its additive inverse is also even.
- If 3/9 is odd, its additive inverse is also odd.
- The sum of the digits of 3/9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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