14/21 Additive Inverse :
The additive inverse of 14/21 is -14/21.
This means that when we add 14/21 and -14/21, the result is zero:
14/21 + (-14/21) = 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: 14/21
- Additive inverse: -14/21
To verify: 14/21 + (-14/21) = 0
Extended Mathematical Exploration of 14/21
Let's explore various mathematical operations and concepts related to 14/21 and its additive inverse -14/21.
Basic Operations and Properties
- Square of 14/21: 0.44444444444444
- Cube of 14/21: 0.2962962962963
- Square root of |14/21|: 0.81649658092773
- Reciprocal of 14/21: 1.5
- Double of 14/21: 1.3333333333333
- Half of 14/21: 0.33333333333333
- Absolute value of 14/21: 0.66666666666667
Trigonometric Functions
- Sine of 14/21: 0.61836980306974
- Cosine of 14/21: 0.78588726077695
- Tangent of 14/21: 0.78684288947298
Exponential and Logarithmic Functions
- e^14/21: 1.9477340410547
- Natural log of 14/21: -0.40546510810816
Floor and Ceiling Functions
- Floor of 14/21: 0
- Ceiling of 14/21: 1
Interesting Properties and Relationships
- The sum of 14/21 and its additive inverse (-14/21) is always 0.
- The product of 14/21 and its additive inverse is: -196
- The average of 14/21 and its additive inverse is always 0.
- The distance between 14/21 and its additive inverse on a number line is: 28
Applications in Algebra
Consider the equation: x + 14/21 = 0
The solution to this equation is x = -14/21, which is the additive inverse of 14/21.
Graphical Representation
On a coordinate plane:
- The point (14/21, 0) is reflected across the y-axis to (-14/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 14/21 and Its Additive Inverse
Consider the alternating series: 14/21 + (-14/21) + 14/21 + (-14/21) + ...
The sum of this series oscillates between 0 and 14/21, never converging unless 14/21 is 0.
In Number Theory
For integer values:
- If 14/21 is even, its additive inverse is also even.
- If 14/21 is odd, its additive inverse is also odd.
- The sum of the digits of 14/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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