67/68 Additive Inverse :
The additive inverse of 67/68 is -67/68.
This means that when we add 67/68 and -67/68, the result is zero:
67/68 + (-67/68) = 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: 67/68
- Additive inverse: -67/68
To verify: 67/68 + (-67/68) = 0
Extended Mathematical Exploration of 67/68
Let's explore various mathematical operations and concepts related to 67/68 and its additive inverse -67/68.
Basic Operations and Properties
- Square of 67/68: 0.9708044982699
- Cube of 67/68: 0.95652796153063
- Square root of |67/68|: 0.99261982533448
- Reciprocal of 67/68: 1.0149253731343
- Double of 67/68: 1.9705882352941
- Half of 67/68: 0.49264705882353
- Absolute value of 67/68: 0.98529411764706
Trigonometric Functions
- Sine of 67/68: 0.83343466118052
- Cosine of 67/68: 0.55261801051261
- Tangent of 67/68: 1.5081568919685
Exponential and Logarithmic Functions
- e^67/68: 2.6785995919854
- Natural log of 67/68: -0.014815085785141
Floor and Ceiling Functions
- Floor of 67/68: 0
- Ceiling of 67/68: 1
Interesting Properties and Relationships
- The sum of 67/68 and its additive inverse (-67/68) is always 0.
- The product of 67/68 and its additive inverse is: -4489
- The average of 67/68 and its additive inverse is always 0.
- The distance between 67/68 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/68 = 0
The solution to this equation is x = -67/68, which is the additive inverse of 67/68.
Graphical Representation
On a coordinate plane:
- The point (67/68, 0) is reflected across the y-axis to (-67/68, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/68 and Its Additive Inverse
Consider the alternating series: 67/68 + (-67/68) + 67/68 + (-67/68) + ...
The sum of this series oscillates between 0 and 67/68, never converging unless 67/68 is 0.
In Number Theory
For integer values:
- If 67/68 is even, its additive inverse is also even.
- If 67/68 is odd, its additive inverse is also odd.
- The sum of the digits of 67/68 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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