72/75 Additive Inverse :
The additive inverse of 72/75 is -72/75.
This means that when we add 72/75 and -72/75, the result is zero:
72/75 + (-72/75) = 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: 72/75
- Additive inverse: -72/75
To verify: 72/75 + (-72/75) = 0
Extended Mathematical Exploration of 72/75
Let's explore various mathematical operations and concepts related to 72/75 and its additive inverse -72/75.
Basic Operations and Properties
- Square of 72/75: 0.9216
- Cube of 72/75: 0.884736
- Square root of |72/75|: 0.97979589711327
- Reciprocal of 72/75: 1.0416666666667
- Double of 72/75: 1.92
- Half of 72/75: 0.48
- Absolute value of 72/75: 0.96
Trigonometric Functions
- Sine of 72/75: 0.819191568301
- Cosine of 72/75: 0.57351998607246
- Tangent of 72/75: 1.4283574909236
Exponential and Logarithmic Functions
- e^72/75: 2.6116964734231
- Natural log of 72/75: -0.040821994520255
Floor and Ceiling Functions
- Floor of 72/75: 0
- Ceiling of 72/75: 1
Interesting Properties and Relationships
- The sum of 72/75 and its additive inverse (-72/75) is always 0.
- The product of 72/75 and its additive inverse is: -5184
- The average of 72/75 and its additive inverse is always 0.
- The distance between 72/75 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72/75 = 0
The solution to this equation is x = -72/75, which is the additive inverse of 72/75.
Graphical Representation
On a coordinate plane:
- The point (72/75, 0) is reflected across the y-axis to (-72/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72/75 and Its Additive Inverse
Consider the alternating series: 72/75 + (-72/75) + 72/75 + (-72/75) + ...
The sum of this series oscillates between 0 and 72/75, never converging unless 72/75 is 0.
In Number Theory
For integer values:
- If 72/75 is even, its additive inverse is also even.
- If 72/75 is odd, its additive inverse is also odd.
- The sum of the digits of 72/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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