7/21 Additive Inverse :
The additive inverse of 7/21 is -7/21.
This means that when we add 7/21 and -7/21, the result is zero:
7/21 + (-7/21) = 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: 7/21
- Additive inverse: -7/21
To verify: 7/21 + (-7/21) = 0
Extended Mathematical Exploration of 7/21
Let's explore various mathematical operations and concepts related to 7/21 and its additive inverse -7/21.
Basic Operations and Properties
- Square of 7/21: 0.11111111111111
- Cube of 7/21: 0.037037037037037
- Square root of |7/21|: 0.57735026918963
- Reciprocal of 7/21: 3
- Double of 7/21: 0.66666666666667
- Half of 7/21: 0.16666666666667
- Absolute value of 7/21: 0.33333333333333
Trigonometric Functions
- Sine of 7/21: 0.32719469679615
- Cosine of 7/21: 0.94495694631474
- Tangent of 7/21: 0.34625354951058
Exponential and Logarithmic Functions
- e^7/21: 1.3956124250861
- Natural log of 7/21: -1.0986122886681
Floor and Ceiling Functions
- Floor of 7/21: 0
- Ceiling of 7/21: 1
Interesting Properties and Relationships
- The sum of 7/21 and its additive inverse (-7/21) is always 0.
- The product of 7/21 and its additive inverse is: -49
- The average of 7/21 and its additive inverse is always 0.
- The distance between 7/21 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7/21 = 0
The solution to this equation is x = -7/21, which is the additive inverse of 7/21.
Graphical Representation
On a coordinate plane:
- The point (7/21, 0) is reflected across the y-axis to (-7/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7/21 and Its Additive Inverse
Consider the alternating series: 7/21 + (-7/21) + 7/21 + (-7/21) + ...
The sum of this series oscillates between 0 and 7/21, never converging unless 7/21 is 0.
In Number Theory
For integer values:
- If 7/21 is even, its additive inverse is also even.
- If 7/21 is odd, its additive inverse is also odd.
- The sum of the digits of 7/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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