10/11 Additive Inverse :
The additive inverse of 10/11 is -10/11.
This means that when we add 10/11 and -10/11, the result is zero:
10/11 + (-10/11) = 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: 10/11
- Additive inverse: -10/11
To verify: 10/11 + (-10/11) = 0
Extended Mathematical Exploration of 10/11
Let's explore various mathematical operations and concepts related to 10/11 and its additive inverse -10/11.
Basic Operations and Properties
- Square of 10/11: 0.82644628099174
- Cube of 10/11: 0.75131480090158
- Square root of |10/11|: 0.95346258924559
- Reciprocal of 10/11: 1.1
- Double of 10/11: 1.8181818181818
- Half of 10/11: 0.45454545454545
- Absolute value of 10/11: 0.90909090909091
Trigonometric Functions
- Sine of 10/11: 0.78894546284426
- Cosine of 10/11: 0.61446322644847
- Tangent of 10/11: 1.2839587934404
Exponential and Logarithmic Functions
- e^10/11: 2.482065084623
- Natural log of 10/11: -0.095310179804325
Floor and Ceiling Functions
- Floor of 10/11: 0
- Ceiling of 10/11: 1
Interesting Properties and Relationships
- The sum of 10/11 and its additive inverse (-10/11) is always 0.
- The product of 10/11 and its additive inverse is: -100
- The average of 10/11 and its additive inverse is always 0.
- The distance between 10/11 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/11 = 0
The solution to this equation is x = -10/11, which is the additive inverse of 10/11.
Graphical Representation
On a coordinate plane:
- The point (10/11, 0) is reflected across the y-axis to (-10/11, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/11 and Its Additive Inverse
Consider the alternating series: 10/11 + (-10/11) + 10/11 + (-10/11) + ...
The sum of this series oscillates between 0 and 10/11, never converging unless 10/11 is 0.
In Number Theory
For integer values:
- If 10/11 is even, its additive inverse is also even.
- If 10/11 is odd, its additive inverse is also odd.
- The sum of the digits of 10/11 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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