65/72 Additive Inverse :
The additive inverse of 65/72 is -65/72.
This means that when we add 65/72 and -65/72, the result is zero:
65/72 + (-65/72) = 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: 65/72
- Additive inverse: -65/72
To verify: 65/72 + (-65/72) = 0
Extended Mathematical Exploration of 65/72
Let's explore various mathematical operations and concepts related to 65/72 and its additive inverse -65/72.
Basic Operations and Properties
- Square of 65/72: 0.81500771604938
- Cube of 65/72: 0.7357708547668
- Square root of |65/72|: 0.95014618758262
- Reciprocal of 65/72: 1.1076923076923
- Double of 65/72: 1.8055555555556
- Half of 65/72: 0.45138888888889
- Absolute value of 65/72: 0.90277777777778
Trigonometric Functions
- Sine of 65/72: 0.78505057967063
- Cosine of 65/72: 0.61943166480154
- Tangent of 65/72: 1.2673723741943
Exponential and Logarithmic Functions
- e^65/72: 2.4664448400232
- Natural log of 65/72: -0.10227884912042
Floor and Ceiling Functions
- Floor of 65/72: 0
- Ceiling of 65/72: 1
Interesting Properties and Relationships
- The sum of 65/72 and its additive inverse (-65/72) is always 0.
- The product of 65/72 and its additive inverse is: -4225
- The average of 65/72 and its additive inverse is always 0.
- The distance between 65/72 and its additive inverse on a number line is: 130
Applications in Algebra
Consider the equation: x + 65/72 = 0
The solution to this equation is x = -65/72, which is the additive inverse of 65/72.
Graphical Representation
On a coordinate plane:
- The point (65/72, 0) is reflected across the y-axis to (-65/72, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 65/72 and Its Additive Inverse
Consider the alternating series: 65/72 + (-65/72) + 65/72 + (-65/72) + ...
The sum of this series oscillates between 0 and 65/72, never converging unless 65/72 is 0.
In Number Theory
For integer values:
- If 65/72 is even, its additive inverse is also even.
- If 65/72 is odd, its additive inverse is also odd.
- The sum of the digits of 65/72 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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