75/85 Additive Inverse :
The additive inverse of 75/85 is -75/85.
This means that when we add 75/85 and -75/85, the result is zero:
75/85 + (-75/85) = 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: 75/85
- Additive inverse: -75/85
To verify: 75/85 + (-75/85) = 0
Extended Mathematical Exploration of 75/85
Let's explore various mathematical operations and concepts related to 75/85 and its additive inverse -75/85.
Basic Operations and Properties
- Square of 75/85: 0.77854671280277
- Cube of 75/85: 0.6869529818848
- Square root of |75/85|: 0.93933643662772
- Reciprocal of 75/85: 1.1333333333333
- Double of 75/85: 1.7647058823529
- Half of 75/85: 0.44117647058824
- Absolute value of 75/85: 0.88235294117647
Trigonometric Functions
- Sine of 75/85: 0.77223592314622
- Cosine of 75/85: 0.63533587888809
- Tangent of 75/85: 1.2154766459872
Exponential and Logarithmic Functions
- e^75/85: 2.416579090617
- Natural log of 75/85: -0.12516314295401
Floor and Ceiling Functions
- Floor of 75/85: 0
- Ceiling of 75/85: 1
Interesting Properties and Relationships
- The sum of 75/85 and its additive inverse (-75/85) is always 0.
- The product of 75/85 and its additive inverse is: -5625
- The average of 75/85 and its additive inverse is always 0.
- The distance between 75/85 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/85 = 0
The solution to this equation is x = -75/85, which is the additive inverse of 75/85.
Graphical Representation
On a coordinate plane:
- The point (75/85, 0) is reflected across the y-axis to (-75/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/85 and Its Additive Inverse
Consider the alternating series: 75/85 + (-75/85) + 75/85 + (-75/85) + ...
The sum of this series oscillates between 0 and 75/85, never converging unless 75/85 is 0.
In Number Theory
For integer values:
- If 75/85 is even, its additive inverse is also even.
- If 75/85 is odd, its additive inverse is also odd.
- The sum of the digits of 75/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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