67/69 Additive Inverse :
The additive inverse of 67/69 is -67/69.
This means that when we add 67/69 and -67/69, the result is zero:
67/69 + (-67/69) = 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: 67/69
- Additive inverse: -67/69
To verify: 67/69 + (-67/69) = 0
Extended Mathematical Exploration of 67/69
Let's explore various mathematical operations and concepts related to 67/69 and its additive inverse -67/69.
Basic Operations and Properties
- Square of 67/69: 0.94286914513758
- Cube of 67/69: 0.91553960469881
- Square root of |67/69|: 0.98540067624983
- Reciprocal of 67/69: 1.0298507462687
- Double of 67/69: 1.9420289855072
- Half of 67/69: 0.48550724637681
- Absolute value of 67/69: 0.97101449275362
Trigonometric Functions
- Sine of 67/69: 0.82545878103375
- Cosine of 67/69: 0.5644623998233
- Tangent of 67/69: 1.462380454911
Exponential and Logarithmic Functions
- e^67/69: 2.6406219928321
- Natural log of 67/69: -0.029413885206293
Floor and Ceiling Functions
- Floor of 67/69: 0
- Ceiling of 67/69: 1
Interesting Properties and Relationships
- The sum of 67/69 and its additive inverse (-67/69) is always 0.
- The product of 67/69 and its additive inverse is: -4489
- The average of 67/69 and its additive inverse is always 0.
- The distance between 67/69 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/69 = 0
The solution to this equation is x = -67/69, which is the additive inverse of 67/69.
Graphical Representation
On a coordinate plane:
- The point (67/69, 0) is reflected across the y-axis to (-67/69, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/69 and Its Additive Inverse
Consider the alternating series: 67/69 + (-67/69) + 67/69 + (-67/69) + ...
The sum of this series oscillates between 0 and 67/69, never converging unless 67/69 is 0.
In Number Theory
For integer values:
- If 67/69 is even, its additive inverse is also even.
- If 67/69 is odd, its additive inverse is also odd.
- The sum of the digits of 67/69 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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