1/3 Additive Inverse :
The additive inverse of 1/3 is -1/3.
This means that when we add 1/3 and -1/3, the result is zero:
1/3 + (-1/3) = 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: 1/3
- Additive inverse: -1/3
To verify: 1/3 + (-1/3) = 0
Extended Mathematical Exploration of 1/3
Let's explore various mathematical operations and concepts related to 1/3 and its additive inverse -1/3.
Basic Operations and Properties
- Square of 1/3: 0.11111111111111
- Cube of 1/3: 0.037037037037037
- Square root of |1/3|: 0.57735026918963
- Reciprocal of 1/3: 3
- Double of 1/3: 0.66666666666667
- Half of 1/3: 0.16666666666667
- Absolute value of 1/3: 0.33333333333333
Trigonometric Functions
- Sine of 1/3: 0.32719469679615
- Cosine of 1/3: 0.94495694631474
- Tangent of 1/3: 0.34625354951058
Exponential and Logarithmic Functions
- e^1/3: 1.3956124250861
- Natural log of 1/3: -1.0986122886681
Floor and Ceiling Functions
- Floor of 1/3: 0
- Ceiling of 1/3: 1
Interesting Properties and Relationships
- The sum of 1/3 and its additive inverse (-1/3) is always 0.
- The product of 1/3 and its additive inverse is: -1
- The average of 1/3 and its additive inverse is always 0.
- The distance between 1/3 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/3 = 0
The solution to this equation is x = -1/3, which is the additive inverse of 1/3.
Graphical Representation
On a coordinate plane:
- The point (1/3, 0) is reflected across the y-axis to (-1/3, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/3 and Its Additive Inverse
Consider the alternating series: 1/3 + (-1/3) + 1/3 + (-1/3) + ...
The sum of this series oscillates between 0 and 1/3, never converging unless 1/3 is 0.
In Number Theory
For integer values:
- If 1/3 is even, its additive inverse is also even.
- If 1/3 is odd, its additive inverse is also odd.
- The sum of the digits of 1/3 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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