16/21 Additive Inverse :
The additive inverse of 16/21 is -16/21.
This means that when we add 16/21 and -16/21, the result is zero:
16/21 + (-16/21) = 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: 16/21
- Additive inverse: -16/21
To verify: 16/21 + (-16/21) = 0
Extended Mathematical Exploration of 16/21
Let's explore various mathematical operations and concepts related to 16/21 and its additive inverse -16/21.
Basic Operations and Properties
- Square of 16/21: 0.58049886621315
- Cube of 16/21: 0.44228485044812
- Square root of |16/21|: 0.87287156094397
- Reciprocal of 16/21: 1.3125
- Double of 16/21: 1.5238095238095
- Half of 16/21: 0.38095238095238
- Absolute value of 16/21: 0.76190476190476
Trigonometric Functions
- Sine of 16/21: 0.69030083455242
- Cosine of 16/21: 0.72352246531551
- Tangent of 16/21: 0.95408348412705
Exponential and Logarithmic Functions
- e^16/21: 2.1423530090066
- Natural log of 16/21: -0.27193371548364
Floor and Ceiling Functions
- Floor of 16/21: 0
- Ceiling of 16/21: 1
Interesting Properties and Relationships
- The sum of 16/21 and its additive inverse (-16/21) is always 0.
- The product of 16/21 and its additive inverse is: -256
- The average of 16/21 and its additive inverse is always 0.
- The distance between 16/21 and its additive inverse on a number line is: 32
Applications in Algebra
Consider the equation: x + 16/21 = 0
The solution to this equation is x = -16/21, which is the additive inverse of 16/21.
Graphical Representation
On a coordinate plane:
- The point (16/21, 0) is reflected across the y-axis to (-16/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 16/21 and Its Additive Inverse
Consider the alternating series: 16/21 + (-16/21) + 16/21 + (-16/21) + ...
The sum of this series oscillates between 0 and 16/21, never converging unless 16/21 is 0.
In Number Theory
For integer values:
- If 16/21 is even, its additive inverse is also even.
- If 16/21 is odd, its additive inverse is also odd.
- The sum of the digits of 16/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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