75/83 Additive Inverse :
The additive inverse of 75/83 is -75/83.
This means that when we add 75/83 and -75/83, the result is zero:
75/83 + (-75/83) = 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: 75/83
- Additive inverse: -75/83
To verify: 75/83 + (-75/83) = 0
Extended Mathematical Exploration of 75/83
Let's explore various mathematical operations and concepts related to 75/83 and its additive inverse -75/83.
Basic Operations and Properties
- Square of 75/83: 0.8165190884018
- Cube of 75/83: 0.73781845337512
- Square root of |75/83|: 0.95058637578672
- Reciprocal of 75/83: 1.1066666666667
- Double of 75/83: 1.8072289156627
- Half of 75/83: 0.45180722891566
- Absolute value of 75/83: 0.90361445783133
Trigonometric Functions
- Sine of 75/83: 0.7855685709478
- Cosine of 75/83: 0.61877461190569
- Tangent of 75/83: 1.2695552723607
Exponential and Logarithmic Functions
- e^75/83: 2.4685093287619
- Natural log of 75/83: -0.10135249426029
Floor and Ceiling Functions
- Floor of 75/83: 0
- Ceiling of 75/83: 1
Interesting Properties and Relationships
- The sum of 75/83 and its additive inverse (-75/83) is always 0.
- The product of 75/83 and its additive inverse is: -5625
- The average of 75/83 and its additive inverse is always 0.
- The distance between 75/83 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/83 = 0
The solution to this equation is x = -75/83, which is the additive inverse of 75/83.
Graphical Representation
On a coordinate plane:
- The point (75/83, 0) is reflected across the y-axis to (-75/83, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/83 and Its Additive Inverse
Consider the alternating series: 75/83 + (-75/83) + 75/83 + (-75/83) + ...
The sum of this series oscillates between 0 and 75/83, never converging unless 75/83 is 0.
In Number Theory
For integer values:
- If 75/83 is even, its additive inverse is also even.
- If 75/83 is odd, its additive inverse is also odd.
- The sum of the digits of 75/83 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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