67/74 Additive Inverse :
The additive inverse of 67/74 is -67/74.
This means that when we add 67/74 and -67/74, the result is zero:
67/74 + (-67/74) = 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: 67/74
- Additive inverse: -67/74
To verify: 67/74 + (-67/74) = 0
Extended Mathematical Exploration of 67/74
Let's explore various mathematical operations and concepts related to 67/74 and its additive inverse -67/74.
Basic Operations and Properties
- Square of 67/74: 0.81975894813733
- Cube of 67/74: 0.74221418277298
- Square root of |67/74|: 0.95152793201535
- Reciprocal of 67/74: 1.1044776119403
- Double of 67/74: 1.8108108108108
- Half of 67/74: 0.4527027027027
- Absolute value of 67/74: 0.90540540540541
Trigonometric Functions
- Sine of 67/74: 0.78667550339288
- Cosine of 67/74: 0.61736670817396
- Tangent of 67/74: 1.2742434811875
Exponential and Logarithmic Functions
- e^67/74: 2.4729342607837
- Natural log of 67/74: -0.099372473813204
Floor and Ceiling Functions
- Floor of 67/74: 0
- Ceiling of 67/74: 1
Interesting Properties and Relationships
- The sum of 67/74 and its additive inverse (-67/74) is always 0.
- The product of 67/74 and its additive inverse is: -4489
- The average of 67/74 and its additive inverse is always 0.
- The distance between 67/74 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/74 = 0
The solution to this equation is x = -67/74, which is the additive inverse of 67/74.
Graphical Representation
On a coordinate plane:
- The point (67/74, 0) is reflected across the y-axis to (-67/74, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/74 and Its Additive Inverse
Consider the alternating series: 67/74 + (-67/74) + 67/74 + (-67/74) + ...
The sum of this series oscillates between 0 and 67/74, never converging unless 67/74 is 0.
In Number Theory
For integer values:
- If 67/74 is even, its additive inverse is also even.
- If 67/74 is odd, its additive inverse is also odd.
- The sum of the digits of 67/74 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: