65/75 Additive Inverse :
The additive inverse of 65/75 is -65/75.
This means that when we add 65/75 and -65/75, the result is zero:
65/75 + (-65/75) = 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: 65/75
- Additive inverse: -65/75
To verify: 65/75 + (-65/75) = 0
Extended Mathematical Exploration of 65/75
Let's explore various mathematical operations and concepts related to 65/75 and its additive inverse -65/75.
Basic Operations and Properties
- Square of 65/75: 0.75111111111111
- Cube of 65/75: 0.65096296296296
- Square root of |65/75|: 0.93094933625126
- Reciprocal of 65/75: 1.1538461538462
- Double of 65/75: 1.7333333333333
- Half of 65/75: 0.43333333333333
- Absolute value of 65/75: 0.86666666666667
Trigonometric Functions
- Sine of 65/75: 0.76217527291384
- Cosine of 65/75: 0.64737072327895
- Tangent of 65/75: 1.1773397305541
Exponential and Logarithmic Functions
- e^65/75: 2.3789677299066
- Natural log of 65/75: -0.14310084364067
Floor and Ceiling Functions
- Floor of 65/75: 0
- Ceiling of 65/75: 1
Interesting Properties and Relationships
- The sum of 65/75 and its additive inverse (-65/75) is always 0.
- The product of 65/75 and its additive inverse is: -4225
- The average of 65/75 and its additive inverse is always 0.
- The distance between 65/75 and its additive inverse on a number line is: 130
Applications in Algebra
Consider the equation: x + 65/75 = 0
The solution to this equation is x = -65/75, which is the additive inverse of 65/75.
Graphical Representation
On a coordinate plane:
- The point (65/75, 0) is reflected across the y-axis to (-65/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 65/75 and Its Additive Inverse
Consider the alternating series: 65/75 + (-65/75) + 65/75 + (-65/75) + ...
The sum of this series oscillates between 0 and 65/75, never converging unless 65/75 is 0.
In Number Theory
For integer values:
- If 65/75 is even, its additive inverse is also even.
- If 65/75 is odd, its additive inverse is also odd.
- The sum of the digits of 65/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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