73/83 Additive Inverse :
The additive inverse of 73/83 is -73/83.
This means that when we add 73/83 and -73/83, the result is zero:
73/83 + (-73/83) = 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: 73/83
- Additive inverse: -73/83
To verify: 73/83 + (-73/83) = 0
Extended Mathematical Exploration of 73/83
Let's explore various mathematical operations and concepts related to 73/83 and its additive inverse -73/83.
Basic Operations and Properties
- Square of 73/83: 0.77355203948323
- Cube of 73/83: 0.68035299858164
- Square root of |73/83|: 0.93782624845392
- Reciprocal of 73/83: 1.1369863013699
- Double of 73/83: 1.7590361445783
- Half of 73/83: 0.43975903614458
- Absolute value of 73/83: 0.87951807228916
Trigonometric Functions
- Sine of 73/83: 0.77043172861476
- Cosine of 73/83: 0.63752251061722
- Tangent of 73/83: 1.2084776863312
Exponential and Logarithmic Functions
- e^73/83: 2.4097381069666
- Natural log of 73/83: -0.12838116664821
Floor and Ceiling Functions
- Floor of 73/83: 0
- Ceiling of 73/83: 1
Interesting Properties and Relationships
- The sum of 73/83 and its additive inverse (-73/83) is always 0.
- The product of 73/83 and its additive inverse is: -5329
- The average of 73/83 and its additive inverse is always 0.
- The distance between 73/83 and its additive inverse on a number line is: 146
Applications in Algebra
Consider the equation: x + 73/83 = 0
The solution to this equation is x = -73/83, which is the additive inverse of 73/83.
Graphical Representation
On a coordinate plane:
- The point (73/83, 0) is reflected across the y-axis to (-73/83, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 73/83 and Its Additive Inverse
Consider the alternating series: 73/83 + (-73/83) + 73/83 + (-73/83) + ...
The sum of this series oscillates between 0 and 73/83, never converging unless 73/83 is 0.
In Number Theory
For integer values:
- If 73/83 is even, its additive inverse is also even.
- If 73/83 is odd, its additive inverse is also odd.
- The sum of the digits of 73/83 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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