78/84 Additive Inverse :
The additive inverse of 78/84 is -78/84.
This means that when we add 78/84 and -78/84, the result is zero:
78/84 + (-78/84) = 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: 78/84
- Additive inverse: -78/84
To verify: 78/84 + (-78/84) = 0
Extended Mathematical Exploration of 78/84
Let's explore various mathematical operations and concepts related to 78/84 and its additive inverse -78/84.
Basic Operations and Properties
- Square of 78/84: 0.86224489795918
- Cube of 78/84: 0.80065597667638
- Square root of |78/84|: 0.96362411165943
- Reciprocal of 78/84: 1.0769230769231
- Double of 78/84: 1.8571428571429
- Half of 78/84: 0.46428571428571
- Absolute value of 78/84: 0.92857142857143
Trigonometric Functions
- Sine of 78/84: 0.80076507464875
- Cosine of 78/84: 0.59897854320733
- Tangent of 78/84: 1.3368844071791
Exponential and Logarithmic Functions
- e^78/84: 2.530891035224
- Natural log of 78/84: -0.074107972153722
Floor and Ceiling Functions
- Floor of 78/84: 0
- Ceiling of 78/84: 1
Interesting Properties and Relationships
- The sum of 78/84 and its additive inverse (-78/84) is always 0.
- The product of 78/84 and its additive inverse is: -6084
- The average of 78/84 and its additive inverse is always 0.
- The distance between 78/84 and its additive inverse on a number line is: 156
Applications in Algebra
Consider the equation: x + 78/84 = 0
The solution to this equation is x = -78/84, which is the additive inverse of 78/84.
Graphical Representation
On a coordinate plane:
- The point (78/84, 0) is reflected across the y-axis to (-78/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 78/84 and Its Additive Inverse
Consider the alternating series: 78/84 + (-78/84) + 78/84 + (-78/84) + ...
The sum of this series oscillates between 0 and 78/84, never converging unless 78/84 is 0.
In Number Theory
For integer values:
- If 78/84 is even, its additive inverse is also even.
- If 78/84 is odd, its additive inverse is also odd.
- The sum of the digits of 78/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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