65/73 Additive Inverse :
The additive inverse of 65/73 is -65/73.
This means that when we add 65/73 and -65/73, the result is zero:
65/73 + (-65/73) = 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: 65/73
- Additive inverse: -65/73
To verify: 65/73 + (-65/73) = 0
Extended Mathematical Exploration of 65/73
Let's explore various mathematical operations and concepts related to 65/73 and its additive inverse -65/73.
Basic Operations and Properties
- Square of 65/73: 0.79283167573654
- Cube of 65/73: 0.70594601264212
- Square root of |65/73|: 0.94361589585175
- Reciprocal of 65/73: 1.1230769230769
- Double of 65/73: 1.7808219178082
- Half of 65/73: 0.44520547945205
- Absolute value of 65/73: 0.89041095890411
Trigonometric Functions
- Sine of 65/73: 0.77733034437747
- Cosine of 65/73: 0.62909262887908
- Tangent of 65/73: 1.2356373428862
Exponential and Logarithmic Functions
- e^65/73: 2.436130595162
- Natural log of 65/73: -0.11607217125275
Floor and Ceiling Functions
- Floor of 65/73: 0
- Ceiling of 65/73: 1
Interesting Properties and Relationships
- The sum of 65/73 and its additive inverse (-65/73) is always 0.
- The product of 65/73 and its additive inverse is: -4225
- The average of 65/73 and its additive inverse is always 0.
- The distance between 65/73 and its additive inverse on a number line is: 130
Applications in Algebra
Consider the equation: x + 65/73 = 0
The solution to this equation is x = -65/73, which is the additive inverse of 65/73.
Graphical Representation
On a coordinate plane:
- The point (65/73, 0) is reflected across the y-axis to (-65/73, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 65/73 and Its Additive Inverse
Consider the alternating series: 65/73 + (-65/73) + 65/73 + (-65/73) + ...
The sum of this series oscillates between 0 and 65/73, never converging unless 65/73 is 0.
In Number Theory
For integer values:
- If 65/73 is even, its additive inverse is also even.
- If 65/73 is odd, its additive inverse is also odd.
- The sum of the digits of 65/73 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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