68/74 Additive Inverse :
The additive inverse of 68/74 is -68/74.
This means that when we add 68/74 and -68/74, the result is zero:
68/74 + (-68/74) = 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: 68/74
- Additive inverse: -68/74
To verify: 68/74 + (-68/74) = 0
Extended Mathematical Exploration of 68/74
Let's explore various mathematical operations and concepts related to 68/74 and its additive inverse -68/74.
Basic Operations and Properties
- Square of 68/74: 0.84441197954711
- Cube of 68/74: 0.77594614336762
- Square root of |68/74|: 0.95860258653882
- Reciprocal of 68/74: 1.0882352941176
- Double of 68/74: 1.8378378378378
- Half of 68/74: 0.45945945945946
- Absolute value of 68/74: 0.91891891891892
Trigonometric Functions
- Sine of 68/74: 0.79494621452985
- Cosine of 68/74: 0.60667991231345
- Tangent of 68/74: 1.3103222941707
Exponential and Logarithmic Functions
- e^68/74: 2.5065791093899
- Natural log of 68/74: -0.084557388028063
Floor and Ceiling Functions
- Floor of 68/74: 0
- Ceiling of 68/74: 1
Interesting Properties and Relationships
- The sum of 68/74 and its additive inverse (-68/74) is always 0.
- The product of 68/74 and its additive inverse is: -4624
- The average of 68/74 and its additive inverse is always 0.
- The distance between 68/74 and its additive inverse on a number line is: 136
Applications in Algebra
Consider the equation: x + 68/74 = 0
The solution to this equation is x = -68/74, which is the additive inverse of 68/74.
Graphical Representation
On a coordinate plane:
- The point (68/74, 0) is reflected across the y-axis to (-68/74, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 68/74 and Its Additive Inverse
Consider the alternating series: 68/74 + (-68/74) + 68/74 + (-68/74) + ...
The sum of this series oscillates between 0 and 68/74, never converging unless 68/74 is 0.
In Number Theory
For integer values:
- If 68/74 is even, its additive inverse is also even.
- If 68/74 is odd, its additive inverse is also odd.
- The sum of the digits of 68/74 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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