21/36 Additive Inverse :
The additive inverse of 21/36 is -21/36.
This means that when we add 21/36 and -21/36, the result is zero:
21/36 + (-21/36) = 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: 21/36
- Additive inverse: -21/36
To verify: 21/36 + (-21/36) = 0
Extended Mathematical Exploration of 21/36
Let's explore various mathematical operations and concepts related to 21/36 and its additive inverse -21/36.
Basic Operations and Properties
- Square of 21/36: 0.34027777777778
- Cube of 21/36: 0.19849537037037
- Square root of |21/36|: 0.76376261582597
- Reciprocal of 21/36: 1.7142857142857
- Double of 21/36: 1.1666666666667
- Half of 21/36: 0.29166666666667
- Absolute value of 21/36: 0.58333333333333
Trigonometric Functions
- Sine of 21/36: 0.55080909588697
- Cosine of 21/36: 0.83463125983166
- Tangent of 21/36: 0.65994304598424
Exponential and Logarithmic Functions
- e^21/36: 1.7920018256558
- Natural log of 21/36: -0.53899650073269
Floor and Ceiling Functions
- Floor of 21/36: 0
- Ceiling of 21/36: 1
Interesting Properties and Relationships
- The sum of 21/36 and its additive inverse (-21/36) is always 0.
- The product of 21/36 and its additive inverse is: -441
- The average of 21/36 and its additive inverse is always 0.
- The distance between 21/36 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/36 = 0
The solution to this equation is x = -21/36, which is the additive inverse of 21/36.
Graphical Representation
On a coordinate plane:
- The point (21/36, 0) is reflected across the y-axis to (-21/36, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/36 and Its Additive Inverse
Consider the alternating series: 21/36 + (-21/36) + 21/36 + (-21/36) + ...
The sum of this series oscillates between 0 and 21/36, never converging unless 21/36 is 0.
In Number Theory
For integer values:
- If 21/36 is even, its additive inverse is also even.
- If 21/36 is odd, its additive inverse is also odd.
- The sum of the digits of 21/36 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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