7/9 Additive Inverse :
The additive inverse of 7/9 is -7/9.
This means that when we add 7/9 and -7/9, the result is zero:
7/9 + (-7/9) = 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: 7/9
- Additive inverse: -7/9
To verify: 7/9 + (-7/9) = 0
Extended Mathematical Exploration of 7/9
Let's explore various mathematical operations and concepts related to 7/9 and its additive inverse -7/9.
Basic Operations and Properties
- Square of 7/9: 0.60493827160494
- Cube of 7/9: 0.47050754458162
- Square root of |7/9|: 0.8819171036882
- Reciprocal of 7/9: 1.2857142857143
- Double of 7/9: 1.5555555555556
- Half of 7/9: 0.38888888888889
- Absolute value of 7/9: 0.77777777777778
Trigonometric Functions
- Sine of 7/9: 0.70169787614674
- Cosine of 7/9: 0.71247462453842
- Tangent of 7/9: 0.98487420039883
Exponential and Logarithmic Functions
- e^7/9: 2.1766299317162
- Natural log of 7/9: -0.25131442828091
Floor and Ceiling Functions
- Floor of 7/9: 0
- Ceiling of 7/9: 1
Interesting Properties and Relationships
- The sum of 7/9 and its additive inverse (-7/9) is always 0.
- The product of 7/9 and its additive inverse is: -49
- The average of 7/9 and its additive inverse is always 0.
- The distance between 7/9 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7/9 = 0
The solution to this equation is x = -7/9, which is the additive inverse of 7/9.
Graphical Representation
On a coordinate plane:
- The point (7/9, 0) is reflected across the y-axis to (-7/9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7/9 and Its Additive Inverse
Consider the alternating series: 7/9 + (-7/9) + 7/9 + (-7/9) + ...
The sum of this series oscillates between 0 and 7/9, never converging unless 7/9 is 0.
In Number Theory
For integer values:
- If 7/9 is even, its additive inverse is also even.
- If 7/9 is odd, its additive inverse is also odd.
- The sum of the digits of 7/9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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