14/15 Additive Inverse :
The additive inverse of 14/15 is -14/15.
This means that when we add 14/15 and -14/15, the result is zero:
14/15 + (-14/15) = 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: 14/15
- Additive inverse: -14/15
To verify: 14/15 + (-14/15) = 0
Extended Mathematical Exploration of 14/15
Let's explore various mathematical operations and concepts related to 14/15 and its additive inverse -14/15.
Basic Operations and Properties
- Square of 14/15: 0.87111111111111
- Cube of 14/15: 0.81303703703704
- Square root of |14/15|: 0.9660917830793
- Reciprocal of 14/15: 1.0714285714286
- Double of 14/15: 1.8666666666667
- Half of 14/15: 0.46666666666667
- Absolute value of 14/15: 0.93333333333333
Trigonometric Functions
- Sine of 14/15: 0.80360826369441
- Cosine of 14/15: 0.59515859946913
- Tangent of 14/15: 1.3502422117587
Exponential and Logarithmic Functions
- e^14/15: 2.542971637808
- Natural log of 14/15: -0.068992871486951
Floor and Ceiling Functions
- Floor of 14/15: 0
- Ceiling of 14/15: 1
Interesting Properties and Relationships
- The sum of 14/15 and its additive inverse (-14/15) is always 0.
- The product of 14/15 and its additive inverse is: -196
- The average of 14/15 and its additive inverse is always 0.
- The distance between 14/15 and its additive inverse on a number line is: 28
Applications in Algebra
Consider the equation: x + 14/15 = 0
The solution to this equation is x = -14/15, which is the additive inverse of 14/15.
Graphical Representation
On a coordinate plane:
- The point (14/15, 0) is reflected across the y-axis to (-14/15, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 14/15 and Its Additive Inverse
Consider the alternating series: 14/15 + (-14/15) + 14/15 + (-14/15) + ...
The sum of this series oscillates between 0 and 14/15, never converging unless 14/15 is 0.
In Number Theory
For integer values:
- If 14/15 is even, its additive inverse is also even.
- If 14/15 is odd, its additive inverse is also odd.
- The sum of the digits of 14/15 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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