10/23 Additive Inverse :
The additive inverse of 10/23 is -10/23.
This means that when we add 10/23 and -10/23, the result is zero:
10/23 + (-10/23) = 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: 10/23
- Additive inverse: -10/23
To verify: 10/23 + (-10/23) = 0
Extended Mathematical Exploration of 10/23
Let's explore various mathematical operations and concepts related to 10/23 and its additive inverse -10/23.
Basic Operations and Properties
- Square of 10/23: 0.1890359168242
- Cube of 10/23: 0.082189529053999
- Square root of |10/23|: 0.65938047339579
- Reciprocal of 10/23: 2.3
- Double of 10/23: 0.8695652173913
- Half of 10/23: 0.21739130434783
- Absolute value of 10/23: 0.43478260869565
Trigonometric Functions
- Sine of 10/23: 0.42121324574912
- Cosine of 10/23: 0.90696163182656
- Tangent of 10/23: 0.46442234265282
Exponential and Logarithmic Functions
- e^10/23: 1.5446272339208
- Natural log of 10/23: -0.8329091229351
Floor and Ceiling Functions
- Floor of 10/23: 0
- Ceiling of 10/23: 1
Interesting Properties and Relationships
- The sum of 10/23 and its additive inverse (-10/23) is always 0.
- The product of 10/23 and its additive inverse is: -100
- The average of 10/23 and its additive inverse is always 0.
- The distance between 10/23 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/23 = 0
The solution to this equation is x = -10/23, which is the additive inverse of 10/23.
Graphical Representation
On a coordinate plane:
- The point (10/23, 0) is reflected across the y-axis to (-10/23, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/23 and Its Additive Inverse
Consider the alternating series: 10/23 + (-10/23) + 10/23 + (-10/23) + ...
The sum of this series oscillates between 0 and 10/23, never converging unless 10/23 is 0.
In Number Theory
For integer values:
- If 10/23 is even, its additive inverse is also even.
- If 10/23 is odd, its additive inverse is also odd.
- The sum of the digits of 10/23 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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