73/85 Additive Inverse :
The additive inverse of 73/85 is -73/85.
This means that when we add 73/85 and -73/85, the result is zero:
73/85 + (-73/85) = 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: 73/85
- Additive inverse: -73/85
To verify: 73/85 + (-73/85) = 0
Extended Mathematical Exploration of 73/85
Let's explore various mathematical operations and concepts related to 73/85 and its additive inverse -73/85.
Basic Operations and Properties
- Square of 73/85: 0.73757785467128
- Cube of 73/85: 0.63344921636475
- Square root of |73/85|: 0.92672732203802
- Reciprocal of 73/85: 1.1643835616438
- Double of 73/85: 1.7176470588235
- Half of 73/85: 0.42941176470588
- Absolute value of 73/85: 0.85882352941176
Trigonometric Functions
- Sine of 73/85: 0.75707446512192
- Cosine of 73/85: 0.65332859593037
- Tangent of 73/85: 1.158795849191
Exponential and Logarithmic Functions
- e^73/85: 2.3603821394186
- Natural log of 73/85: -0.15219181534193
Floor and Ceiling Functions
- Floor of 73/85: 0
- Ceiling of 73/85: 1
Interesting Properties and Relationships
- The sum of 73/85 and its additive inverse (-73/85) is always 0.
- The product of 73/85 and its additive inverse is: -5329
- The average of 73/85 and its additive inverse is always 0.
- The distance between 73/85 and its additive inverse on a number line is: 146
Applications in Algebra
Consider the equation: x + 73/85 = 0
The solution to this equation is x = -73/85, which is the additive inverse of 73/85.
Graphical Representation
On a coordinate plane:
- The point (73/85, 0) is reflected across the y-axis to (-73/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 73/85 and Its Additive Inverse
Consider the alternating series: 73/85 + (-73/85) + 73/85 + (-73/85) + ...
The sum of this series oscillates between 0 and 73/85, never converging unless 73/85 is 0.
In Number Theory
For integer values:
- If 73/85 is even, its additive inverse is also even.
- If 73/85 is odd, its additive inverse is also odd.
- The sum of the digits of 73/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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