74/78 Additive Inverse :
The additive inverse of 74/78 is -74/78.
This means that when we add 74/78 and -74/78, the result is zero:
74/78 + (-74/78) = 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: 74/78
- Additive inverse: -74/78
To verify: 74/78 + (-74/78) = 0
Extended Mathematical Exploration of 74/78
Let's explore various mathematical operations and concepts related to 74/78 and its additive inverse -74/78.
Basic Operations and Properties
- Square of 74/78: 0.90006574621959
- Cube of 74/78: 0.85390852846474
- Square root of |74/78|: 0.97402153401141
- Reciprocal of 74/78: 1.0540540540541
- Double of 74/78: 1.8974358974359
- Half of 74/78: 0.47435897435897
- Absolute value of 74/78: 0.94871794871795
Trigonometric Functions
- Sine of 74/78: 0.81266908895573
- Cosine of 74/78: 0.58272545152572
- Tangent of 74/78: 1.3946002990396
Exponential and Logarithmic Functions
- e^74/78: 2.5823967710322
- Natural log of 74/78: -0.052643733485422
Floor and Ceiling Functions
- Floor of 74/78: 0
- Ceiling of 74/78: 1
Interesting Properties and Relationships
- The sum of 74/78 and its additive inverse (-74/78) is always 0.
- The product of 74/78 and its additive inverse is: -5476
- The average of 74/78 and its additive inverse is always 0.
- The distance between 74/78 and its additive inverse on a number line is: 148
Applications in Algebra
Consider the equation: x + 74/78 = 0
The solution to this equation is x = -74/78, which is the additive inverse of 74/78.
Graphical Representation
On a coordinate plane:
- The point (74/78, 0) is reflected across the y-axis to (-74/78, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 74/78 and Its Additive Inverse
Consider the alternating series: 74/78 + (-74/78) + 74/78 + (-74/78) + ...
The sum of this series oscillates between 0 and 74/78, never converging unless 74/78 is 0.
In Number Theory
For integer values:
- If 74/78 is even, its additive inverse is also even.
- If 74/78 is odd, its additive inverse is also odd.
- The sum of the digits of 74/78 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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