2/3 Additive Inverse :
The additive inverse of 2/3 is -2/3.
This means that when we add 2/3 and -2/3, the result is zero:
2/3 + (-2/3) = 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: 2/3
- Additive inverse: -2/3
To verify: 2/3 + (-2/3) = 0
Extended Mathematical Exploration of 2/3
Let's explore various mathematical operations and concepts related to 2/3 and its additive inverse -2/3.
Basic Operations and Properties
- Square of 2/3: 0.44444444444444
- Cube of 2/3: 0.2962962962963
- Square root of |2/3|: 0.81649658092773
- Reciprocal of 2/3: 1.5
- Double of 2/3: 1.3333333333333
- Half of 2/3: 0.33333333333333
- Absolute value of 2/3: 0.66666666666667
Trigonometric Functions
- Sine of 2/3: 0.61836980306974
- Cosine of 2/3: 0.78588726077695
- Tangent of 2/3: 0.78684288947298
Exponential and Logarithmic Functions
- e^2/3: 1.9477340410547
- Natural log of 2/3: -0.40546510810816
Floor and Ceiling Functions
- Floor of 2/3: 0
- Ceiling of 2/3: 1
Interesting Properties and Relationships
- The sum of 2/3 and its additive inverse (-2/3) is always 0.
- The product of 2/3 and its additive inverse is: -4
- The average of 2/3 and its additive inverse is always 0.
- The distance between 2/3 and its additive inverse on a number line is: 4
Applications in Algebra
Consider the equation: x + 2/3 = 0
The solution to this equation is x = -2/3, which is the additive inverse of 2/3.
Graphical Representation
On a coordinate plane:
- The point (2/3, 0) is reflected across the y-axis to (-2/3, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 2/3 and Its Additive Inverse
Consider the alternating series: 2/3 + (-2/3) + 2/3 + (-2/3) + ...
The sum of this series oscillates between 0 and 2/3, never converging unless 2/3 is 0.
In Number Theory
For integer values:
- If 2/3 is even, its additive inverse is also even.
- If 2/3 is odd, its additive inverse is also odd.
- The sum of the digits of 2/3 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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