9/21 Additive Inverse :
The additive inverse of 9/21 is -9/21.
This means that when we add 9/21 and -9/21, the result is zero:
9/21 + (-9/21) = 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: 9/21
- Additive inverse: -9/21
To verify: 9/21 + (-9/21) = 0
Extended Mathematical Exploration of 9/21
Let's explore various mathematical operations and concepts related to 9/21 and its additive inverse -9/21.
Basic Operations and Properties
- Square of 9/21: 0.18367346938776
- Cube of 9/21: 0.078717201166181
- Square root of |9/21|: 0.65465367070798
- Reciprocal of 9/21: 2.3333333333333
- Double of 9/21: 0.85714285714286
- Half of 9/21: 0.21428571428571
- Absolute value of 9/21: 0.42857142857143
Trigonometric Functions
- Sine of 9/21: 0.41557185499305
- Cosine of 9/21: 0.90956035167417
- Tangent of 9/21: 0.45689310690394
Exponential and Logarithmic Functions
- e^9/21: 1.5350630092552
- Natural log of 9/21: -0.8472978603872
Floor and Ceiling Functions
- Floor of 9/21: 0
- Ceiling of 9/21: 1
Interesting Properties and Relationships
- The sum of 9/21 and its additive inverse (-9/21) is always 0.
- The product of 9/21 and its additive inverse is: -81
- The average of 9/21 and its additive inverse is always 0.
- The distance between 9/21 and its additive inverse on a number line is: 18
Applications in Algebra
Consider the equation: x + 9/21 = 0
The solution to this equation is x = -9/21, which is the additive inverse of 9/21.
Graphical Representation
On a coordinate plane:
- The point (9/21, 0) is reflected across the y-axis to (-9/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 9/21 and Its Additive Inverse
Consider the alternating series: 9/21 + (-9/21) + 9/21 + (-9/21) + ...
The sum of this series oscillates between 0 and 9/21, never converging unless 9/21 is 0.
In Number Theory
For integer values:
- If 9/21 is even, its additive inverse is also even.
- If 9/21 is odd, its additive inverse is also odd.
- The sum of the digits of 9/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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