84/96 Additive Inverse :
The additive inverse of 84/96 is -84/96.
This means that when we add 84/96 and -84/96, the result is zero:
84/96 + (-84/96) = 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: 84/96
- Additive inverse: -84/96
To verify: 84/96 + (-84/96) = 0
Extended Mathematical Exploration of 84/96
Let's explore various mathematical operations and concepts related to 84/96 and its additive inverse -84/96.
Basic Operations and Properties
- Square of 84/96: 0.765625
- Cube of 84/96: 0.669921875
- Square root of |84/96|: 0.93541434669349
- Reciprocal of 84/96: 1.1428571428571
- Double of 84/96: 1.75
- Half of 84/96: 0.4375
- Absolute value of 84/96: 0.875
Trigonometric Functions
- Sine of 84/96: 0.76754350223603
- Cosine of 84/96: 0.64099685816333
- Tangent of 84/96: 1.1974216292343
Exponential and Logarithmic Functions
- e^84/96: 2.3988752939671
- Natural log of 84/96: -0.13353139262452
Floor and Ceiling Functions
- Floor of 84/96: 0
- Ceiling of 84/96: 1
Interesting Properties and Relationships
- The sum of 84/96 and its additive inverse (-84/96) is always 0.
- The product of 84/96 and its additive inverse is: -7056
- The average of 84/96 and its additive inverse is always 0.
- The distance between 84/96 and its additive inverse on a number line is: 168
Applications in Algebra
Consider the equation: x + 84/96 = 0
The solution to this equation is x = -84/96, which is the additive inverse of 84/96.
Graphical Representation
On a coordinate plane:
- The point (84/96, 0) is reflected across the y-axis to (-84/96, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 84/96 and Its Additive Inverse
Consider the alternating series: 84/96 + (-84/96) + 84/96 + (-84/96) + ...
The sum of this series oscillates between 0 and 84/96, never converging unless 84/96 is 0.
In Number Theory
For integer values:
- If 84/96 is even, its additive inverse is also even.
- If 84/96 is odd, its additive inverse is also odd.
- The sum of the digits of 84/96 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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