71/72 Additive Inverse :
The additive inverse of 71/72 is -71/72.
This means that when we add 71/72 and -71/72, the result is zero:
71/72 + (-71/72) = 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: 71/72
- Additive inverse: -71/72
To verify: 71/72 + (-71/72) = 0
Extended Mathematical Exploration of 71/72
Let's explore various mathematical operations and concepts related to 71/72 and its additive inverse -71/72.
Basic Operations and Properties
- Square of 71/72: 0.97241512345679
- Cube of 71/72: 0.95890935785322
- Square root of |71/72|: 0.99303127398442
- Reciprocal of 71/72: 1.0140845070423
- Double of 71/72: 1.9722222222222
- Half of 71/72: 0.49305555555556
- Absolute value of 71/72: 0.98611111111111
Trigonometric Functions
- Sine of 71/72: 0.83388586828323
- Cosine of 71/72: 0.5519369154872
- Tangent of 71/72: 1.5108354684831
Exponential and Logarithmic Functions
- e^71/72: 2.680788884542
- Natural log of 71/72: -0.01398624197474
Floor and Ceiling Functions
- Floor of 71/72: 0
- Ceiling of 71/72: 1
Interesting Properties and Relationships
- The sum of 71/72 and its additive inverse (-71/72) is always 0.
- The product of 71/72 and its additive inverse is: -5041
- The average of 71/72 and its additive inverse is always 0.
- The distance between 71/72 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/72 = 0
The solution to this equation is x = -71/72, which is the additive inverse of 71/72.
Graphical Representation
On a coordinate plane:
- The point (71/72, 0) is reflected across the y-axis to (-71/72, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/72 and Its Additive Inverse
Consider the alternating series: 71/72 + (-71/72) + 71/72 + (-71/72) + ...
The sum of this series oscillates between 0 and 71/72, never converging unless 71/72 is 0.
In Number Theory
For integer values:
- If 71/72 is even, its additive inverse is also even.
- If 71/72 is odd, its additive inverse is also odd.
- The sum of the digits of 71/72 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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