65/74 Additive Inverse :
The additive inverse of 65/74 is -65/74.
This means that when we add 65/74 and -65/74, the result is zero:
65/74 + (-65/74) = 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: 65/74
- Additive inverse: -65/74
To verify: 65/74 + (-65/74) = 0
Extended Mathematical Exploration of 65/74
Let's explore various mathematical operations and concepts related to 65/74 and its additive inverse -65/74.
Basic Operations and Properties
- Square of 65/74: 0.77154857560263
- Cube of 65/74: 0.67771158667799
- Square root of |65/74|: 0.93721842618377
- Reciprocal of 65/74: 1.1384615384615
- Double of 65/74: 1.7567567567568
- Half of 65/74: 0.43918918918919
- Absolute value of 65/74: 0.87837837837838
Trigonometric Functions
- Sine of 65/74: 0.76970464789103
- Cosine of 65/74: 0.63840015273725
- Tangent of 65/74: 1.2056774181378
Exponential and Logarithmic Functions
- e^65/74: 2.4069933075322
- Natural log of 65/74: -0.12967782330853
Floor and Ceiling Functions
- Floor of 65/74: 0
- Ceiling of 65/74: 1
Interesting Properties and Relationships
- The sum of 65/74 and its additive inverse (-65/74) is always 0.
- The product of 65/74 and its additive inverse is: -4225
- The average of 65/74 and its additive inverse is always 0.
- The distance between 65/74 and its additive inverse on a number line is: 130
Applications in Algebra
Consider the equation: x + 65/74 = 0
The solution to this equation is x = -65/74, which is the additive inverse of 65/74.
Graphical Representation
On a coordinate plane:
- The point (65/74, 0) is reflected across the y-axis to (-65/74, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 65/74 and Its Additive Inverse
Consider the alternating series: 65/74 + (-65/74) + 65/74 + (-65/74) + ...
The sum of this series oscillates between 0 and 65/74, never converging unless 65/74 is 0.
In Number Theory
For integer values:
- If 65/74 is even, its additive inverse is also even.
- If 65/74 is odd, its additive inverse is also odd.
- The sum of the digits of 65/74 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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