75/88 Additive Inverse :
The additive inverse of 75/88 is -75/88.
This means that when we add 75/88 and -75/88, the result is zero:
75/88 + (-75/88) = 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: 75/88
- Additive inverse: -75/88
To verify: 75/88 + (-75/88) = 0
Extended Mathematical Exploration of 75/88
Let's explore various mathematical operations and concepts related to 75/88 and its additive inverse -75/88.
Basic Operations and Properties
- Square of 75/88: 0.72636880165289
- Cube of 75/88: 0.61906431959053
- Square root of |75/88|: 0.923186182345
- Reciprocal of 75/88: 1.1733333333333
- Double of 75/88: 1.7045454545455
- Half of 75/88: 0.42613636363636
- Absolute value of 75/88: 0.85227272727273
Trigonometric Functions
- Sine of 75/88: 0.75277842525473
- Cosine of 75/88: 0.65827398738748
- Tangent of 75/88: 1.1435639865435
Exponential and Logarithmic Functions
- e^75/88: 2.3449702781915
- Natural log of 75/88: -0.1598487009419
Floor and Ceiling Functions
- Floor of 75/88: 0
- Ceiling of 75/88: 1
Interesting Properties and Relationships
- The sum of 75/88 and its additive inverse (-75/88) is always 0.
- The product of 75/88 and its additive inverse is: -5625
- The average of 75/88 and its additive inverse is always 0.
- The distance between 75/88 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/88 = 0
The solution to this equation is x = -75/88, which is the additive inverse of 75/88.
Graphical Representation
On a coordinate plane:
- The point (75/88, 0) is reflected across the y-axis to (-75/88, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/88 and Its Additive Inverse
Consider the alternating series: 75/88 + (-75/88) + 75/88 + (-75/88) + ...
The sum of this series oscillates between 0 and 75/88, never converging unless 75/88 is 0.
In Number Theory
For integer values:
- If 75/88 is even, its additive inverse is also even.
- If 75/88 is odd, its additive inverse is also odd.
- The sum of the digits of 75/88 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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