67/78 Additive Inverse :
The additive inverse of 67/78 is -67/78.
This means that when we add 67/78 and -67/78, the result is zero:
67/78 + (-67/78) = 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: 67/78
- Additive inverse: -67/78
To verify: 67/78 + (-67/78) = 0
Extended Mathematical Exploration of 67/78
Let's explore various mathematical operations and concepts related to 67/78 and its additive inverse -67/78.
Basic Operations and Properties
- Square of 67/78: 0.73783694937541
- Cube of 67/78: 0.63378302061734
- Square root of |67/78|: 0.9268086959963
- Reciprocal of 67/78: 1.1641791044776
- Double of 67/78: 1.7179487179487
- Half of 67/78: 0.42948717948718
- Absolute value of 67/78: 0.85897435897436
Trigonometric Functions
- Sine of 67/78: 0.75717299777635
- Cosine of 67/78: 0.65321439928891
- Tangent of 67/78: 1.1591492756446
Exponential and Logarithmic Functions
- e^67/78: 2.3607381816744
- Natural log of 67/78: -0.15201620729863
Floor and Ceiling Functions
- Floor of 67/78: 0
- Ceiling of 67/78: 1
Interesting Properties and Relationships
- The sum of 67/78 and its additive inverse (-67/78) is always 0.
- The product of 67/78 and its additive inverse is: -4489
- The average of 67/78 and its additive inverse is always 0.
- The distance between 67/78 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/78 = 0
The solution to this equation is x = -67/78, which is the additive inverse of 67/78.
Graphical Representation
On a coordinate plane:
- The point (67/78, 0) is reflected across the y-axis to (-67/78, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/78 and Its Additive Inverse
Consider the alternating series: 67/78 + (-67/78) + 67/78 + (-67/78) + ...
The sum of this series oscillates between 0 and 67/78, never converging unless 67/78 is 0.
In Number Theory
For integer values:
- If 67/78 is even, its additive inverse is also even.
- If 67/78 is odd, its additive inverse is also odd.
- The sum of the digits of 67/78 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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