67/71 Additive Inverse :
The additive inverse of 67/71 is -67/71.
This means that when we add 67/71 and -67/71, the result is zero:
67/71 + (-67/71) = 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: 67/71
- Additive inverse: -67/71
To verify: 67/71 + (-67/71) = 0
Extended Mathematical Exploration of 67/71
Let's explore various mathematical operations and concepts related to 67/71 and its additive inverse -67/71.
Basic Operations and Properties
- Square of 67/71: 0.89049791707994
- Cube of 67/71: 0.84032902034305
- Square root of |67/71|: 0.97142265355044
- Reciprocal of 67/71: 1.0597014925373
- Double of 67/71: 1.887323943662
- Half of 67/71: 0.47183098591549
- Absolute value of 67/71: 0.94366197183099
Trigonometric Functions
- Sine of 67/71: 0.80971246802567
- Cosine of 67/71: 0.58682682208961
- Tangent of 67/71: 1.3798150281243
Exponential and Logarithmic Functions
- e^67/71: 2.5693731838661
- Natural log of 67/71: -0.057987257650349
Floor and Ceiling Functions
- Floor of 67/71: 0
- Ceiling of 67/71: 1
Interesting Properties and Relationships
- The sum of 67/71 and its additive inverse (-67/71) is always 0.
- The product of 67/71 and its additive inverse is: -4489
- The average of 67/71 and its additive inverse is always 0.
- The distance between 67/71 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/71 = 0
The solution to this equation is x = -67/71, which is the additive inverse of 67/71.
Graphical Representation
On a coordinate plane:
- The point (67/71, 0) is reflected across the y-axis to (-67/71, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/71 and Its Additive Inverse
Consider the alternating series: 67/71 + (-67/71) + 67/71 + (-67/71) + ...
The sum of this series oscillates between 0 and 67/71, never converging unless 67/71 is 0.
In Number Theory
For integer values:
- If 67/71 is even, its additive inverse is also even.
- If 67/71 is odd, its additive inverse is also odd.
- The sum of the digits of 67/71 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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