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