71/84 Additive Inverse :
The additive inverse of 71/84 is -71/84.
This means that when we add 71/84 and -71/84, the result is zero:
71/84 + (-71/84) = 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: 71/84
- Additive inverse: -71/84
To verify: 71/84 + (-71/84) = 0
Extended Mathematical Exploration of 71/84
Let's explore various mathematical operations and concepts related to 71/84 and its additive inverse -71/84.
Basic Operations and Properties
- Square of 71/84: 0.71442743764172
- Cube of 71/84: 0.60386128657812
- Square root of |71/84|: 0.91936831315752
- Reciprocal of 71/84: 1.1830985915493
- Double of 71/84: 1.6904761904762
- Half of 71/84: 0.42261904761905
- Absolute value of 71/84: 0.8452380952381
Trigonometric Functions
- Sine of 71/84: 0.74812912223025
- Cosine of 71/84: 0.66355317531529
- Tangent of 71/84: 1.1274591849776
Exponential and Logarithmic Functions
- e^71/84: 2.3285321609933
- Natural log of 71/84: -0.168136921802
Floor and Ceiling Functions
- Floor of 71/84: 0
- Ceiling of 71/84: 1
Interesting Properties and Relationships
- The sum of 71/84 and its additive inverse (-71/84) is always 0.
- The product of 71/84 and its additive inverse is: -5041
- The average of 71/84 and its additive inverse is always 0.
- The distance between 71/84 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/84 = 0
The solution to this equation is x = -71/84, which is the additive inverse of 71/84.
Graphical Representation
On a coordinate plane:
- The point (71/84, 0) is reflected across the y-axis to (-71/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/84 and Its Additive Inverse
Consider the alternating series: 71/84 + (-71/84) + 71/84 + (-71/84) + ...
The sum of this series oscillates between 0 and 71/84, never converging unless 71/84 is 0.
In Number Theory
For integer values:
- If 71/84 is even, its additive inverse is also even.
- If 71/84 is odd, its additive inverse is also odd.
- The sum of the digits of 71/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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