14/16 Additive Inverse :
The additive inverse of 14/16 is -14/16.
This means that when we add 14/16 and -14/16, the result is zero:
14/16 + (-14/16) = 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: 14/16
- Additive inverse: -14/16
To verify: 14/16 + (-14/16) = 0
Extended Mathematical Exploration of 14/16
Let's explore various mathematical operations and concepts related to 14/16 and its additive inverse -14/16.
Basic Operations and Properties
- Square of 14/16: 0.765625
- Cube of 14/16: 0.669921875
- Square root of |14/16|: 0.93541434669349
- Reciprocal of 14/16: 1.1428571428571
- Double of 14/16: 1.75
- Half of 14/16: 0.4375
- Absolute value of 14/16: 0.875
Trigonometric Functions
- Sine of 14/16: 0.76754350223603
- Cosine of 14/16: 0.64099685816333
- Tangent of 14/16: 1.1974216292343
Exponential and Logarithmic Functions
- e^14/16: 2.3988752939671
- Natural log of 14/16: -0.13353139262452
Floor and Ceiling Functions
- Floor of 14/16: 0
- Ceiling of 14/16: 1
Interesting Properties and Relationships
- The sum of 14/16 and its additive inverse (-14/16) is always 0.
- The product of 14/16 and its additive inverse is: -196
- The average of 14/16 and its additive inverse is always 0.
- The distance between 14/16 and its additive inverse on a number line is: 28
Applications in Algebra
Consider the equation: x + 14/16 = 0
The solution to this equation is x = -14/16, which is the additive inverse of 14/16.
Graphical Representation
On a coordinate plane:
- The point (14/16, 0) is reflected across the y-axis to (-14/16, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 14/16 and Its Additive Inverse
Consider the alternating series: 14/16 + (-14/16) + 14/16 + (-14/16) + ...
The sum of this series oscillates between 0 and 14/16, never converging unless 14/16 is 0.
In Number Theory
For integer values:
- If 14/16 is even, its additive inverse is also even.
- If 14/16 is odd, its additive inverse is also odd.
- The sum of the digits of 14/16 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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