67/77 Additive Inverse :
The additive inverse of 67/77 is -67/77.
This means that when we add 67/77 and -67/77, the result is zero:
67/77 + (-67/77) = 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: 67/77
- Additive inverse: -67/77
To verify: 67/77 + (-67/77) = 0
Extended Mathematical Exploration of 67/77
Let's explore various mathematical operations and concepts related to 67/77 and its additive inverse -67/77.
Basic Operations and Properties
- Square of 67/77: 0.75712599089222
- Cube of 67/77: 0.658797940127
- Square root of |67/77|: 0.93280752040808
- Reciprocal of 67/77: 1.1492537313433
- Double of 67/77: 1.7402597402597
- Half of 67/77: 0.43506493506494
- Absolute value of 67/77: 0.87012987012987
Trigonometric Functions
- Sine of 67/77: 0.76441267428702
- Cosine of 67/77: 0.64472727830406
- Tangent of 67/77: 1.1856372454068
Exponential and Logarithmic Functions
- e^67/77: 2.3872208620768
- Natural log of 67/77: -0.13911280246272
Floor and Ceiling Functions
- Floor of 67/77: 0
- Ceiling of 67/77: 1
Interesting Properties and Relationships
- The sum of 67/77 and its additive inverse (-67/77) is always 0.
- The product of 67/77 and its additive inverse is: -4489
- The average of 67/77 and its additive inverse is always 0.
- The distance between 67/77 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/77 = 0
The solution to this equation is x = -67/77, which is the additive inverse of 67/77.
Graphical Representation
On a coordinate plane:
- The point (67/77, 0) is reflected across the y-axis to (-67/77, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/77 and Its Additive Inverse
Consider the alternating series: 67/77 + (-67/77) + 67/77 + (-67/77) + ...
The sum of this series oscillates between 0 and 67/77, never converging unless 67/77 is 0.
In Number Theory
For integer values:
- If 67/77 is even, its additive inverse is also even.
- If 67/77 is odd, its additive inverse is also odd.
- The sum of the digits of 67/77 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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