21/34 Additive Inverse :
The additive inverse of 21/34 is -21/34.
This means that when we add 21/34 and -21/34, the result is zero:
21/34 + (-21/34) = 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: 21/34
- Additive inverse: -21/34
To verify: 21/34 + (-21/34) = 0
Extended Mathematical Exploration of 21/34
Let's explore various mathematical operations and concepts related to 21/34 and its additive inverse -21/34.
Basic Operations and Properties
- Square of 21/34: 0.38148788927336
- Cube of 21/34: 0.23562487278648
- Square root of |21/34|: 0.78590524799338
- Reciprocal of 21/34: 1.6190476190476
- Double of 21/34: 1.2352941176471
- Half of 21/34: 0.30882352941176
- Absolute value of 21/34: 0.61764705882353
Trigonometric Functions
- Sine of 21/34: 0.57911854576991
- Cosine of 21/34: 0.81524334400554
- Tangent of 21/34: 0.71036280152197
Exponential and Logarithmic Functions
- e^21/34: 1.8545592353006
- Natural log of 21/34: -0.48183808689274
Floor and Ceiling Functions
- Floor of 21/34: 0
- Ceiling of 21/34: 1
Interesting Properties and Relationships
- The sum of 21/34 and its additive inverse (-21/34) is always 0.
- The product of 21/34 and its additive inverse is: -441
- The average of 21/34 and its additive inverse is always 0.
- The distance between 21/34 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/34 = 0
The solution to this equation is x = -21/34, which is the additive inverse of 21/34.
Graphical Representation
On a coordinate plane:
- The point (21/34, 0) is reflected across the y-axis to (-21/34, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/34 and Its Additive Inverse
Consider the alternating series: 21/34 + (-21/34) + 21/34 + (-21/34) + ...
The sum of this series oscillates between 0 and 21/34, never converging unless 21/34 is 0.
In Number Theory
For integer values:
- If 21/34 is even, its additive inverse is also even.
- If 21/34 is odd, its additive inverse is also odd.
- The sum of the digits of 21/34 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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