21/30 Additive Inverse :
The additive inverse of 21/30 is -21/30.
This means that when we add 21/30 and -21/30, the result is zero:
21/30 + (-21/30) = 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: 21/30
- Additive inverse: -21/30
To verify: 21/30 + (-21/30) = 0
Extended Mathematical Exploration of 21/30
Let's explore various mathematical operations and concepts related to 21/30 and its additive inverse -21/30.
Basic Operations and Properties
- Square of 21/30: 0.49
- Cube of 21/30: 0.343
- Square root of |21/30|: 0.83666002653408
- Reciprocal of 21/30: 1.4285714285714
- Double of 21/30: 1.4
- Half of 21/30: 0.35
- Absolute value of 21/30: 0.7
Trigonometric Functions
- Sine of 21/30: 0.64421768723769
- Cosine of 21/30: 0.76484218728449
- Tangent of 21/30: 0.84228838046308
Exponential and Logarithmic Functions
- e^21/30: 2.0137527074705
- Natural log of 21/30: -0.35667494393873
Floor and Ceiling Functions
- Floor of 21/30: 0
- Ceiling of 21/30: 1
Interesting Properties and Relationships
- The sum of 21/30 and its additive inverse (-21/30) is always 0.
- The product of 21/30 and its additive inverse is: -441
- The average of 21/30 and its additive inverse is always 0.
- The distance between 21/30 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/30 = 0
The solution to this equation is x = -21/30, which is the additive inverse of 21/30.
Graphical Representation
On a coordinate plane:
- The point (21/30, 0) is reflected across the y-axis to (-21/30, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/30 and Its Additive Inverse
Consider the alternating series: 21/30 + (-21/30) + 21/30 + (-21/30) + ...
The sum of this series oscillates between 0 and 21/30, never converging unless 21/30 is 0.
In Number Theory
For integer values:
- If 21/30 is even, its additive inverse is also even.
- If 21/30 is odd, its additive inverse is also odd.
- The sum of the digits of 21/30 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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