67/73 Additive Inverse :
The additive inverse of 67/73 is -67/73.
This means that when we add 67/73 and -67/73, the result is zero:
67/73 + (-67/73) = 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: 67/73
- Additive inverse: -67/73
To verify: 67/73 + (-67/73) = 0
Extended Mathematical Exploration of 67/73
Let's explore various mathematical operations and concepts related to 67/73 and its additive inverse -67/73.
Basic Operations and Properties
- Square of 67/73: 0.84237192719084
- Cube of 67/73: 0.77313587838064
- Square root of |67/73|: 0.95802307862498
- Reciprocal of 67/73: 1.089552238806
- Double of 67/73: 1.8356164383562
- Half of 67/73: 0.45890410958904
- Absolute value of 67/73: 0.91780821917808
Trigonometric Functions
- Sine of 67/73: 0.79427188510282
- Cosine of 67/73: 0.60756248446988
- Tangent of 67/73: 1.3073089688805
Exponential and Logarithmic Functions
- e^67/73: 2.503796598176
- Natural log of 67/73: -0.085766821757425
Floor and Ceiling Functions
- Floor of 67/73: 0
- Ceiling of 67/73: 1
Interesting Properties and Relationships
- The sum of 67/73 and its additive inverse (-67/73) is always 0.
- The product of 67/73 and its additive inverse is: -4489
- The average of 67/73 and its additive inverse is always 0.
- The distance between 67/73 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/73 = 0
The solution to this equation is x = -67/73, which is the additive inverse of 67/73.
Graphical Representation
On a coordinate plane:
- The point (67/73, 0) is reflected across the y-axis to (-67/73, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/73 and Its Additive Inverse
Consider the alternating series: 67/73 + (-67/73) + 67/73 + (-67/73) + ...
The sum of this series oscillates between 0 and 67/73, never converging unless 67/73 is 0.
In Number Theory
For integer values:
- If 67/73 is even, its additive inverse is also even.
- If 67/73 is odd, its additive inverse is also odd.
- The sum of the digits of 67/73 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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