8/9 Additive Inverse :
The additive inverse of 8/9 is -8/9.
This means that when we add 8/9 and -8/9, the result is zero:
8/9 + (-8/9) = 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: 8/9
- Additive inverse: -8/9
To verify: 8/9 + (-8/9) = 0
Extended Mathematical Exploration of 8/9
Let's explore various mathematical operations and concepts related to 8/9 and its additive inverse -8/9.
Basic Operations and Properties
- Square of 8/9: 0.79012345679012
- Cube of 8/9: 0.70233196159122
- Square root of |8/9|: 0.94280904158206
- Reciprocal of 8/9: 1.125
- Double of 8/9: 1.7777777777778
- Half of 8/9: 0.44444444444444
- Absolute value of 8/9: 0.88888888888889
Trigonometric Functions
- Sine of 8/9: 0.77637192130066
- Cosine of 8/9: 0.63027505092295
- Tangent of 8/9: 1.2317985935883
Exponential and Logarithmic Functions
- e^8/9: 2.4324254542872
- Natural log of 8/9: -0.11778303565638
Floor and Ceiling Functions
- Floor of 8/9: 0
- Ceiling of 8/9: 1
Interesting Properties and Relationships
- The sum of 8/9 and its additive inverse (-8/9) is always 0.
- The product of 8/9 and its additive inverse is: -64
- The average of 8/9 and its additive inverse is always 0.
- The distance between 8/9 and its additive inverse on a number line is: 16
Applications in Algebra
Consider the equation: x + 8/9 = 0
The solution to this equation is x = -8/9, which is the additive inverse of 8/9.
Graphical Representation
On a coordinate plane:
- The point (8/9, 0) is reflected across the y-axis to (-8/9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8/9 and Its Additive Inverse
Consider the alternating series: 8/9 + (-8/9) + 8/9 + (-8/9) + ...
The sum of this series oscillates between 0 and 8/9, never converging unless 8/9 is 0.
In Number Theory
For integer values:
- If 8/9 is even, its additive inverse is also even.
- If 8/9 is odd, its additive inverse is also odd.
- The sum of the digits of 8/9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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