75/87 Additive Inverse :
The additive inverse of 75/87 is -75/87.
This means that when we add 75/87 and -75/87, the result is zero:
75/87 + (-75/87) = 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: 75/87
- Additive inverse: -75/87
To verify: 75/87 + (-75/87) = 0
Extended Mathematical Exploration of 75/87
Let's explore various mathematical operations and concepts related to 75/87 and its additive inverse -75/87.
Basic Operations and Properties
- Square of 75/87: 0.74316290130797
- Cube of 75/87: 0.64065767354135
- Square root of |75/87|: 0.92847669088526
- Reciprocal of 75/87: 1.16
- Double of 75/87: 1.7241379310345
- Half of 75/87: 0.43103448275862
- Absolute value of 75/87: 0.86206896551724
Trigonometric Functions
- Sine of 75/87: 0.75919081053922
- Cosine of 75/87: 0.65086812273517
- Tangent of 75/87: 1.1664280120969
Exponential and Logarithmic Functions
- e^75/87: 2.3680550530772
- Natural log of 75/87: -0.14842000511827
Floor and Ceiling Functions
- Floor of 75/87: 0
- Ceiling of 75/87: 1
Interesting Properties and Relationships
- The sum of 75/87 and its additive inverse (-75/87) is always 0.
- The product of 75/87 and its additive inverse is: -5625
- The average of 75/87 and its additive inverse is always 0.
- The distance between 75/87 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/87 = 0
The solution to this equation is x = -75/87, which is the additive inverse of 75/87.
Graphical Representation
On a coordinate plane:
- The point (75/87, 0) is reflected across the y-axis to (-75/87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/87 and Its Additive Inverse
Consider the alternating series: 75/87 + (-75/87) + 75/87 + (-75/87) + ...
The sum of this series oscillates between 0 and 75/87, never converging unless 75/87 is 0.
In Number Theory
For integer values:
- If 75/87 is even, its additive inverse is also even.
- If 75/87 is odd, its additive inverse is also odd.
- The sum of the digits of 75/87 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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