74/80 Additive Inverse :
The additive inverse of 74/80 is -74/80.
This means that when we add 74/80 and -74/80, the result is zero:
74/80 + (-74/80) = 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: 74/80
- Additive inverse: -74/80
To verify: 74/80 + (-74/80) = 0
Extended Mathematical Exploration of 74/80
Let's explore various mathematical operations and concepts related to 74/80 and its additive inverse -74/80.
Basic Operations and Properties
- Square of 74/80: 0.855625
- Cube of 74/80: 0.791453125
- Square root of |74/80|: 0.96176920308357
- Reciprocal of 74/80: 1.0810810810811
- Double of 74/80: 1.85
- Half of 74/80: 0.4625
- Absolute value of 74/80: 0.925
Trigonometric Functions
- Sine of 74/80: 0.79862076319881
- Cosine of 74/80: 0.60183459238211
- Tangent of 74/80: 1.3269771683243
Exponential and Logarithmic Functions
- e^74/80: 2.5218682603581
- Natural log of 74/80: -0.077961541469712
Floor and Ceiling Functions
- Floor of 74/80: 0
- Ceiling of 74/80: 1
Interesting Properties and Relationships
- The sum of 74/80 and its additive inverse (-74/80) is always 0.
- The product of 74/80 and its additive inverse is: -5476
- The average of 74/80 and its additive inverse is always 0.
- The distance between 74/80 and its additive inverse on a number line is: 148
Applications in Algebra
Consider the equation: x + 74/80 = 0
The solution to this equation is x = -74/80, which is the additive inverse of 74/80.
Graphical Representation
On a coordinate plane:
- The point (74/80, 0) is reflected across the y-axis to (-74/80, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 74/80 and Its Additive Inverse
Consider the alternating series: 74/80 + (-74/80) + 74/80 + (-74/80) + ...
The sum of this series oscillates between 0 and 74/80, never converging unless 74/80 is 0.
In Number Theory
For integer values:
- If 74/80 is even, its additive inverse is also even.
- If 74/80 is odd, its additive inverse is also odd.
- The sum of the digits of 74/80 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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