8/10 Additive Inverse :
The additive inverse of 8/10 is -8/10.
This means that when we add 8/10 and -8/10, the result is zero:
8/10 + (-8/10) = 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: 8/10
- Additive inverse: -8/10
To verify: 8/10 + (-8/10) = 0
Extended Mathematical Exploration of 8/10
Let's explore various mathematical operations and concepts related to 8/10 and its additive inverse -8/10.
Basic Operations and Properties
- Square of 8/10: 0.64
- Cube of 8/10: 0.512
- Square root of |8/10|: 0.89442719099992
- Reciprocal of 8/10: 1.25
- Double of 8/10: 1.6
- Half of 8/10: 0.4
- Absolute value of 8/10: 0.8
Trigonometric Functions
- Sine of 8/10: 0.71735609089952
- Cosine of 8/10: 0.69670670934717
- Tangent of 8/10: 1.0296385570504
Exponential and Logarithmic Functions
- e^8/10: 2.2255409284925
- Natural log of 8/10: -0.22314355131421
Floor and Ceiling Functions
- Floor of 8/10: 0
- Ceiling of 8/10: 1
Interesting Properties and Relationships
- The sum of 8/10 and its additive inverse (-8/10) is always 0.
- The product of 8/10 and its additive inverse is: -64
- The average of 8/10 and its additive inverse is always 0.
- The distance between 8/10 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8/10 = 0
The solution to this equation is x = -8/10, which is the additive inverse of 8/10.
Graphical Representation
On a coordinate plane:
- The point (8/10, 0) is reflected across the y-axis to (-8/10, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8/10 and Its Additive Inverse
Consider the alternating series: 8/10 + (-8/10) + 8/10 + (-8/10) + ...
The sum of this series oscillates between 0 and 8/10, never converging unless 8/10 is 0.
In Number Theory
For integer values:
- If 8/10 is even, its additive inverse is also even.
- If 8/10 is odd, its additive inverse is also odd.
- The sum of the digits of 8/10 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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