8/15 Additive Inverse :
The additive inverse of 8/15 is -8/15.
This means that when we add 8/15 and -8/15, the result is zero:
8/15 + (-8/15) = 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: 8/15
- Additive inverse: -8/15
To verify: 8/15 + (-8/15) = 0
Extended Mathematical Exploration of 8/15
Let's explore various mathematical operations and concepts related to 8/15 and its additive inverse -8/15.
Basic Operations and Properties
- Square of 8/15: 0.28444444444444
- Cube of 8/15: 0.1517037037037
- Square root of |8/15|: 0.73029674334022
- Reciprocal of 8/15: 1.875
- Double of 8/15: 1.0666666666667
- Half of 8/15: 0.26666666666667
- Absolute value of 8/15: 0.53333333333333
Trigonometric Functions
- Sine of 8/15: 0.5084065509313
- Cosine of 8/15: 0.86111716912981
- Tangent of 8/15: 0.59040345397487
Exponential and Logarithmic Functions
- e^8/15: 1.7046048653228
- Natural log of 8/15: -0.62860865942237
Floor and Ceiling Functions
- Floor of 8/15: 0
- Ceiling of 8/15: 1
Interesting Properties and Relationships
- The sum of 8/15 and its additive inverse (-8/15) is always 0.
- The product of 8/15 and its additive inverse is: -64
- The average of 8/15 and its additive inverse is always 0.
- The distance between 8/15 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8/15 = 0
The solution to this equation is x = -8/15, which is the additive inverse of 8/15.
Graphical Representation
On a coordinate plane:
- The point (8/15, 0) is reflected across the y-axis to (-8/15, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8/15 and Its Additive Inverse
Consider the alternating series: 8/15 + (-8/15) + 8/15 + (-8/15) + ...
The sum of this series oscillates between 0 and 8/15, never converging unless 8/15 is 0.
In Number Theory
For integer values:
- If 8/15 is even, its additive inverse is also even.
- If 8/15 is odd, its additive inverse is also odd.
- The sum of the digits of 8/15 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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