15/21 Additive Inverse :
The additive inverse of 15/21 is -15/21.
This means that when we add 15/21 and -15/21, the result is zero:
15/21 + (-15/21) = 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: 15/21
- Additive inverse: -15/21
To verify: 15/21 + (-15/21) = 0
Extended Mathematical Exploration of 15/21
Let's explore various mathematical operations and concepts related to 15/21 and its additive inverse -15/21.
Basic Operations and Properties
- Square of 15/21: 0.51020408163265
- Cube of 15/21: 0.36443148688047
- Square root of |15/21|: 0.84515425472852
- Reciprocal of 15/21: 1.4
- Double of 15/21: 1.4285714285714
- Half of 15/21: 0.35714285714286
- Absolute value of 15/21: 0.71428571428571
Trigonometric Functions
- Sine of 15/21: 0.65507789717852
- Cosine of 15/21: 0.7555613467007
- Tangent of 15/21: 0.8670082185107
Exponential and Logarithmic Functions
- e^15/21: 2.0427270702661
- Natural log of 15/21: -0.33647223662121
Floor and Ceiling Functions
- Floor of 15/21: 0
- Ceiling of 15/21: 1
Interesting Properties and Relationships
- The sum of 15/21 and its additive inverse (-15/21) is always 0.
- The product of 15/21 and its additive inverse is: -225
- The average of 15/21 and its additive inverse is always 0.
- The distance between 15/21 and its additive inverse on a number line is: 30
Applications in Algebra
Consider the equation: x + 15/21 = 0
The solution to this equation is x = -15/21, which is the additive inverse of 15/21.
Graphical Representation
On a coordinate plane:
- The point (15/21, 0) is reflected across the y-axis to (-15/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 15/21 and Its Additive Inverse
Consider the alternating series: 15/21 + (-15/21) + 15/21 + (-15/21) + ...
The sum of this series oscillates between 0 and 15/21, never converging unless 15/21 is 0.
In Number Theory
For integer values:
- If 15/21 is even, its additive inverse is also even.
- If 15/21 is odd, its additive inverse is also odd.
- The sum of the digits of 15/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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