72/84 Additive Inverse :
The additive inverse of 72/84 is -72/84.
This means that when we add 72/84 and -72/84, the result is zero:
72/84 + (-72/84) = 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: 72/84
- Additive inverse: -72/84
To verify: 72/84 + (-72/84) = 0
Extended Mathematical Exploration of 72/84
Let's explore various mathematical operations and concepts related to 72/84 and its additive inverse -72/84.
Basic Operations and Properties
- Square of 72/84: 0.73469387755102
- Cube of 72/84: 0.62973760932945
- Square root of |72/84|: 0.92582009977255
- Reciprocal of 72/84: 1.1666666666667
- Double of 72/84: 1.7142857142857
- Half of 72/84: 0.42857142857143
- Absolute value of 72/84: 0.85714285714286
Trigonometric Functions
- Sine of 72/84: 0.75597536514673
- Cosine of 72/84: 0.65460006667527
- Tangent of 72/84: 1.1548660069443
Exponential and Logarithmic Functions
- e^72/84: 2.3564184423837
- Natural log of 72/84: -0.15415067982726
Floor and Ceiling Functions
- Floor of 72/84: 0
- Ceiling of 72/84: 1
Interesting Properties and Relationships
- The sum of 72/84 and its additive inverse (-72/84) is always 0.
- The product of 72/84 and its additive inverse is: -5184
- The average of 72/84 and its additive inverse is always 0.
- The distance between 72/84 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72/84 = 0
The solution to this equation is x = -72/84, which is the additive inverse of 72/84.
Graphical Representation
On a coordinate plane:
- The point (72/84, 0) is reflected across the y-axis to (-72/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72/84 and Its Additive Inverse
Consider the alternating series: 72/84 + (-72/84) + 72/84 + (-72/84) + ...
The sum of this series oscillates between 0 and 72/84, never converging unless 72/84 is 0.
In Number Theory
For integer values:
- If 72/84 is even, its additive inverse is also even.
- If 72/84 is odd, its additive inverse is also odd.
- The sum of the digits of 72/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: