10/20 Additive Inverse :
The additive inverse of 10/20 is -10/20.
This means that when we add 10/20 and -10/20, the result is zero:
10/20 + (-10/20) = 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: 10/20
- Additive inverse: -10/20
To verify: 10/20 + (-10/20) = 0
Extended Mathematical Exploration of 10/20
Let's explore various mathematical operations and concepts related to 10/20 and its additive inverse -10/20.
Basic Operations and Properties
- Square of 10/20: 0.25
- Cube of 10/20: 0.125
- Square root of |10/20|: 0.70710678118655
- Reciprocal of 10/20: 2
- Double of 10/20: 1
- Half of 10/20: 0.25
- Absolute value of 10/20: 0.5
Trigonometric Functions
- Sine of 10/20: 0.4794255386042
- Cosine of 10/20: 0.87758256189037
- Tangent of 10/20: 0.54630248984379
Exponential and Logarithmic Functions
- e^10/20: 1.6487212707001
- Natural log of 10/20: -0.69314718055995
Floor and Ceiling Functions
- Floor of 10/20: 0
- Ceiling of 10/20: 1
Interesting Properties and Relationships
- The sum of 10/20 and its additive inverse (-10/20) is always 0.
- The product of 10/20 and its additive inverse is: -100
- The average of 10/20 and its additive inverse is always 0.
- The distance between 10/20 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/20 = 0
The solution to this equation is x = -10/20, which is the additive inverse of 10/20.
Graphical Representation
On a coordinate plane:
- The point (10/20, 0) is reflected across the y-axis to (-10/20, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/20 and Its Additive Inverse
Consider the alternating series: 10/20 + (-10/20) + 10/20 + (-10/20) + ...
The sum of this series oscillates between 0 and 10/20, never converging unless 10/20 is 0.
In Number Theory
For integer values:
- If 10/20 is even, its additive inverse is also even.
- If 10/20 is odd, its additive inverse is also odd.
- The sum of the digits of 10/20 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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