60/75 Additive Inverse :
The additive inverse of 60/75 is -60/75.
This means that when we add 60/75 and -60/75, the result is zero:
60/75 + (-60/75) = 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: 60/75
- Additive inverse: -60/75
To verify: 60/75 + (-60/75) = 0
Extended Mathematical Exploration of 60/75
Let's explore various mathematical operations and concepts related to 60/75 and its additive inverse -60/75.
Basic Operations and Properties
- Square of 60/75: 0.64
- Cube of 60/75: 0.512
- Square root of |60/75|: 0.89442719099992
- Reciprocal of 60/75: 1.25
- Double of 60/75: 1.6
- Half of 60/75: 0.4
- Absolute value of 60/75: 0.8
Trigonometric Functions
- Sine of 60/75: 0.71735609089952
- Cosine of 60/75: 0.69670670934717
- Tangent of 60/75: 1.0296385570504
Exponential and Logarithmic Functions
- e^60/75: 2.2255409284925
- Natural log of 60/75: -0.22314355131421
Floor and Ceiling Functions
- Floor of 60/75: 0
- Ceiling of 60/75: 1
Interesting Properties and Relationships
- The sum of 60/75 and its additive inverse (-60/75) is always 0.
- The product of 60/75 and its additive inverse is: -3600
- The average of 60/75 and its additive inverse is always 0.
- The distance between 60/75 and its additive inverse on a number line is: 120
Applications in Algebra
Consider the equation: x + 60/75 = 0
The solution to this equation is x = -60/75, which is the additive inverse of 60/75.
Graphical Representation
On a coordinate plane:
- The point (60/75, 0) is reflected across the y-axis to (-60/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 60/75 and Its Additive Inverse
Consider the alternating series: 60/75 + (-60/75) + 60/75 + (-60/75) + ...
The sum of this series oscillates between 0 and 60/75, never converging unless 60/75 is 0.
In Number Theory
For integer values:
- If 60/75 is even, its additive inverse is also even.
- If 60/75 is odd, its additive inverse is also odd.
- The sum of the digits of 60/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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