75/84 Additive Inverse :
The additive inverse of 75/84 is -75/84.
This means that when we add 75/84 and -75/84, the result is zero:
75/84 + (-75/84) = 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: 75/84
- Additive inverse: -75/84
To verify: 75/84 + (-75/84) = 0
Extended Mathematical Exploration of 75/84
Let's explore various mathematical operations and concepts related to 75/84 and its additive inverse -75/84.
Basic Operations and Properties
- Square of 75/84: 0.79719387755102
- Cube of 75/84: 0.71178024781341
- Square root of |75/84|: 0.94491118252307
- Reciprocal of 75/84: 1.12
- Double of 75/84: 1.7857142857143
- Half of 75/84: 0.44642857142857
- Absolute value of 75/84: 0.89285714285714
Trigonometric Functions
- Sine of 75/84: 0.77886689343679
- Cosine of 75/84: 0.62718925557452
- Tangent of 75/84: 1.2418371113889
Exponential and Logarithmic Functions
- e^75/84: 2.4420971133567
- Natural log of 75/84: -0.113328685307
Floor and Ceiling Functions
- Floor of 75/84: 0
- Ceiling of 75/84: 1
Interesting Properties and Relationships
- The sum of 75/84 and its additive inverse (-75/84) is always 0.
- The product of 75/84 and its additive inverse is: -5625
- The average of 75/84 and its additive inverse is always 0.
- The distance between 75/84 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/84 = 0
The solution to this equation is x = -75/84, which is the additive inverse of 75/84.
Graphical Representation
On a coordinate plane:
- The point (75/84, 0) is reflected across the y-axis to (-75/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/84 and Its Additive Inverse
Consider the alternating series: 75/84 + (-75/84) + 75/84 + (-75/84) + ...
The sum of this series oscillates between 0 and 75/84, never converging unless 75/84 is 0.
In Number Theory
For integer values:
- If 75/84 is even, its additive inverse is also even.
- If 75/84 is odd, its additive inverse is also odd.
- The sum of the digits of 75/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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