67/70 Additive Inverse :
The additive inverse of 67/70 is -67/70.
This means that when we add 67/70 and -67/70, the result is zero:
67/70 + (-67/70) = 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: 67/70
- Additive inverse: -67/70
To verify: 67/70 + (-67/70) = 0
Extended Mathematical Exploration of 67/70
Let's explore various mathematical operations and concepts related to 67/70 and its additive inverse -67/70.
Basic Operations and Properties
- Square of 67/70: 0.91612244897959
- Cube of 67/70: 0.87686005830904
- Square root of |67/70|: 0.97833678104365
- Reciprocal of 67/70: 1.044776119403
- Double of 67/70: 1.9142857142857
- Half of 67/70: 0.47857142857143
- Absolute value of 67/70: 0.95714285714286
Trigonometric Functions
- Sine of 67/70: 0.81754959836201
- Cosine of 67/70: 0.57585818932973
- Tangent of 67/70: 1.4197064720285
Exponential and Logarithmic Functions
- e^67/70: 2.6042451333395
- Natural log of 67/70: -0.043802622658393
Floor and Ceiling Functions
- Floor of 67/70: 0
- Ceiling of 67/70: 1
Interesting Properties and Relationships
- The sum of 67/70 and its additive inverse (-67/70) is always 0.
- The product of 67/70 and its additive inverse is: -4489
- The average of 67/70 and its additive inverse is always 0.
- The distance between 67/70 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/70 = 0
The solution to this equation is x = -67/70, which is the additive inverse of 67/70.
Graphical Representation
On a coordinate plane:
- The point (67/70, 0) is reflected across the y-axis to (-67/70, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/70 and Its Additive Inverse
Consider the alternating series: 67/70 + (-67/70) + 67/70 + (-67/70) + ...
The sum of this series oscillates between 0 and 67/70, never converging unless 67/70 is 0.
In Number Theory
For integer values:
- If 67/70 is even, its additive inverse is also even.
- If 67/70 is odd, its additive inverse is also odd.
- The sum of the digits of 67/70 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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