69/84 Additive Inverse :
The additive inverse of 69/84 is -69/84.
This means that when we add 69/84 and -69/84, the result is zero:
69/84 + (-69/84) = 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: 69/84
- Additive inverse: -69/84
To verify: 69/84 + (-69/84) = 0
Extended Mathematical Exploration of 69/84
Let's explore various mathematical operations and concepts related to 69/84 and its additive inverse -69/84.
Basic Operations and Properties
- Square of 69/84: 0.67474489795918
- Cube of 69/84: 0.55425473760933
- Square root of |69/84|: 0.90632696717497
- Reciprocal of 69/84: 1.2173913043478
- Double of 69/84: 1.6428571428571
- Half of 69/84: 0.41071428571429
- Absolute value of 69/84: 0.82142857142857
Trigonometric Functions
- Sine of 69/84: 0.73211968505305
- Cosine of 69/84: 0.68117601745645
- Tangent of 69/84: 1.0747878173792
Exponential and Logarithmic Functions
- e^69/84: 2.2737457266691
- Natural log of 69/84: -0.19671029424605
Floor and Ceiling Functions
- Floor of 69/84: 0
- Ceiling of 69/84: 1
Interesting Properties and Relationships
- The sum of 69/84 and its additive inverse (-69/84) is always 0.
- The product of 69/84 and its additive inverse is: -4761
- The average of 69/84 and its additive inverse is always 0.
- The distance between 69/84 and its additive inverse on a number line is: 138
Applications in Algebra
Consider the equation: x + 69/84 = 0
The solution to this equation is x = -69/84, which is the additive inverse of 69/84.
Graphical Representation
On a coordinate plane:
- The point (69/84, 0) is reflected across the y-axis to (-69/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 69/84 and Its Additive Inverse
Consider the alternating series: 69/84 + (-69/84) + 69/84 + (-69/84) + ...
The sum of this series oscillates between 0 and 69/84, never converging unless 69/84 is 0.
In Number Theory
For integer values:
- If 69/84 is even, its additive inverse is also even.
- If 69/84 is odd, its additive inverse is also odd.
- The sum of the digits of 69/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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