17/21 Additive Inverse :
The additive inverse of 17/21 is -17/21.
This means that when we add 17/21 and -17/21, the result is zero:
17/21 + (-17/21) = 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: 17/21
- Additive inverse: -17/21
To verify: 17/21 + (-17/21) = 0
Extended Mathematical Exploration of 17/21
Let's explore various mathematical operations and concepts related to 17/21 and its additive inverse -17/21.
Basic Operations and Properties
- Square of 17/21: 0.65532879818594
- Cube of 17/21: 0.53050426519814
- Square root of |17/21|: 0.89973541084244
- Reciprocal of 17/21: 1.2352941176471
- Double of 17/21: 1.6190476190476
- Half of 17/21: 0.4047619047619
- Absolute value of 17/21: 0.80952380952381
Trigonometric Functions
- Sine of 17/21: 0.72395875967671
- Cosine of 17/21: 0.68984325341875
- Tangent of 17/21: 1.0494539971057
Exponential and Logarithmic Functions
- e^17/21: 2.2468378091263
- Natural log of 17/21: -0.21130909366721
Floor and Ceiling Functions
- Floor of 17/21: 0
- Ceiling of 17/21: 1
Interesting Properties and Relationships
- The sum of 17/21 and its additive inverse (-17/21) is always 0.
- The product of 17/21 and its additive inverse is: -289
- The average of 17/21 and its additive inverse is always 0.
- The distance between 17/21 and its additive inverse on a number line is: 34
Applications in Algebra
Consider the equation: x + 17/21 = 0
The solution to this equation is x = -17/21, which is the additive inverse of 17/21.
Graphical Representation
On a coordinate plane:
- The point (17/21, 0) is reflected across the y-axis to (-17/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 17/21 and Its Additive Inverse
Consider the alternating series: 17/21 + (-17/21) + 17/21 + (-17/21) + ...
The sum of this series oscillates between 0 and 17/21, never converging unless 17/21 is 0.
In Number Theory
For integer values:
- If 17/21 is even, its additive inverse is also even.
- If 17/21 is odd, its additive inverse is also odd.
- The sum of the digits of 17/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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