72/87 Additive Inverse :
The additive inverse of 72/87 is -72/87.
This means that when we add 72/87 and -72/87, the result is zero:
72/87 + (-72/87) = 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: 72/87
- Additive inverse: -72/87
To verify: 72/87 + (-72/87) = 0
Extended Mathematical Exploration of 72/87
Let's explore various mathematical operations and concepts related to 72/87 and its additive inverse -72/87.
Basic Operations and Properties
- Square of 72/87: 0.68489892984542
- Cube of 72/87: 0.56681290745828
- Square root of |72/87|: 0.90971765229468
- Reciprocal of 72/87: 1.2083333333333
- Double of 72/87: 1.6551724137931
- Half of 72/87: 0.41379310344828
- Absolute value of 72/87: 0.82758620689655
Trigonometric Functions
- Sine of 72/87: 0.73630021249692
- Cosine of 72/87: 0.67665500594985
- Tangent of 72/87: 1.0881471444423
Exponential and Logarithmic Functions
- e^72/87: 2.2877898188256
- Natural log of 72/87: -0.18924199963853
Floor and Ceiling Functions
- Floor of 72/87: 0
- Ceiling of 72/87: 1
Interesting Properties and Relationships
- The sum of 72/87 and its additive inverse (-72/87) is always 0.
- The product of 72/87 and its additive inverse is: -5184
- The average of 72/87 and its additive inverse is always 0.
- The distance between 72/87 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72/87 = 0
The solution to this equation is x = -72/87, which is the additive inverse of 72/87.
Graphical Representation
On a coordinate plane:
- The point (72/87, 0) is reflected across the y-axis to (-72/87, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72/87 and Its Additive Inverse
Consider the alternating series: 72/87 + (-72/87) + 72/87 + (-72/87) + ...
The sum of this series oscillates between 0 and 72/87, never converging unless 72/87 is 0.
In Number Theory
For integer values:
- If 72/87 is even, its additive inverse is also even.
- If 72/87 is odd, its additive inverse is also odd.
- The sum of the digits of 72/87 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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