69/75 Additive Inverse :
The additive inverse of 69/75 is -69/75.
This means that when we add 69/75 and -69/75, the result is zero:
69/75 + (-69/75) = 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: 69/75
- Additive inverse: -69/75
To verify: 69/75 + (-69/75) = 0
Extended Mathematical Exploration of 69/75
Let's explore various mathematical operations and concepts related to 69/75 and its additive inverse -69/75.
Basic Operations and Properties
- Square of 69/75: 0.8464
- Cube of 69/75: 0.778688
- Square root of |69/75|: 0.95916630466254
- Reciprocal of 69/75: 1.0869565217391
- Double of 69/75: 1.84
- Half of 69/75: 0.46
- Absolute value of 69/75: 0.92
Trigonometric Functions
- Sine of 69/75: 0.79560162003637
- Cosine of 69/75: 0.60582015664346
- Tangent of 69/75: 1.3132636993202
Exponential and Logarithmic Functions
- e^69/75: 2.5092903899363
- Natural log of 69/75: -0.083381608939051
Floor and Ceiling Functions
- Floor of 69/75: 0
- Ceiling of 69/75: 1
Interesting Properties and Relationships
- The sum of 69/75 and its additive inverse (-69/75) is always 0.
- The product of 69/75 and its additive inverse is: -4761
- The average of 69/75 and its additive inverse is always 0.
- The distance between 69/75 and its additive inverse on a number line is: 138
Applications in Algebra
Consider the equation: x + 69/75 = 0
The solution to this equation is x = -69/75, which is the additive inverse of 69/75.
Graphical Representation
On a coordinate plane:
- The point (69/75, 0) is reflected across the y-axis to (-69/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 69/75 and Its Additive Inverse
Consider the alternating series: 69/75 + (-69/75) + 69/75 + (-69/75) + ...
The sum of this series oscillates between 0 and 69/75, never converging unless 69/75 is 0.
In Number Theory
For integer values:
- If 69/75 is even, its additive inverse is also even.
- If 69/75 is odd, its additive inverse is also odd.
- The sum of the digits of 69/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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