21/26 Additive Inverse :
The additive inverse of 21/26 is -21/26.
This means that when we add 21/26 and -21/26, the result is zero:
21/26 + (-21/26) = 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: 21/26
- Additive inverse: -21/26
To verify: 21/26 + (-21/26) = 0
Extended Mathematical Exploration of 21/26
Let's explore various mathematical operations and concepts related to 21/26 and its additive inverse -21/26.
Basic Operations and Properties
- Square of 21/26: 0.65236686390533
- Cube of 21/26: 0.52691169776969
- Square root of |21/26|: 0.89871703427292
- Reciprocal of 21/26: 1.2380952380952
- Double of 21/26: 1.6153846153846
- Half of 21/26: 0.40384615384615
- Absolute value of 21/26: 0.80769230769231
Trigonometric Functions
- Sine of 21/26: 0.72269409697806
- Cosine of 21/26: 0.69116802746732
- Tangent of 21/26: 1.0456127428612
Exponential and Logarithmic Functions
- e^21/26: 2.2427264876594
- Natural log of 21/26: -0.21357410029806
Floor and Ceiling Functions
- Floor of 21/26: 0
- Ceiling of 21/26: 1
Interesting Properties and Relationships
- The sum of 21/26 and its additive inverse (-21/26) is always 0.
- The product of 21/26 and its additive inverse is: -441
- The average of 21/26 and its additive inverse is always 0.
- The distance between 21/26 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/26 = 0
The solution to this equation is x = -21/26, which is the additive inverse of 21/26.
Graphical Representation
On a coordinate plane:
- The point (21/26, 0) is reflected across the y-axis to (-21/26, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/26 and Its Additive Inverse
Consider the alternating series: 21/26 + (-21/26) + 21/26 + (-21/26) + ...
The sum of this series oscillates between 0 and 21/26, never converging unless 21/26 is 0.
In Number Theory
For integer values:
- If 21/26 is even, its additive inverse is also even.
- If 21/26 is odd, its additive inverse is also odd.
- The sum of the digits of 21/26 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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