10/21 Additive Inverse :
The additive inverse of 10/21 is -10/21.
This means that when we add 10/21 and -10/21, the result is zero:
10/21 + (-10/21) = 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: 10/21
- Additive inverse: -10/21
To verify: 10/21 + (-10/21) = 0
Extended Mathematical Exploration of 10/21
Let's explore various mathematical operations and concepts related to 10/21 and its additive inverse -10/21.
Basic Operations and Properties
- Square of 10/21: 0.22675736961451
- Cube of 10/21: 0.10797969981643
- Square root of |10/21|: 0.69006555934235
- Reciprocal of 10/21: 2.1
- Double of 10/21: 0.95238095238095
- Half of 10/21: 0.23809523809524
- Absolute value of 10/21: 0.47619047619048
Trigonometric Functions
- Sine of 10/21: 0.45839680466269
- Cosine of 10/21: 0.88874764105174
- Tangent of 10/21: 0.51577836439624
Exponential and Logarithmic Functions
- e^10/21: 1.60992964002
- Natural log of 10/21: -0.74193734472938
Floor and Ceiling Functions
- Floor of 10/21: 0
- Ceiling of 10/21: 1
Interesting Properties and Relationships
- The sum of 10/21 and its additive inverse (-10/21) is always 0.
- The product of 10/21 and its additive inverse is: -100
- The average of 10/21 and its additive inverse is always 0.
- The distance between 10/21 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/21 = 0
The solution to this equation is x = -10/21, which is the additive inverse of 10/21.
Graphical Representation
On a coordinate plane:
- The point (10/21, 0) is reflected across the y-axis to (-10/21, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/21 and Its Additive Inverse
Consider the alternating series: 10/21 + (-10/21) + 10/21 + (-10/21) + ...
The sum of this series oscillates between 0 and 10/21, never converging unless 10/21 is 0.
In Number Theory
For integer values:
- If 10/21 is even, its additive inverse is also even.
- If 10/21 is odd, its additive inverse is also odd.
- The sum of the digits of 10/21 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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