34/47 Additive Inverse :
The additive inverse of 34/47 is -34/47.
This means that when we add 34/47 and -34/47, the result is zero:
34/47 + (-34/47) = 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: 34/47
- Additive inverse: -34/47
To verify: 34/47 + (-34/47) = 0
Extended Mathematical Exploration of 34/47
Let's explore various mathematical operations and concepts related to 34/47 and its additive inverse -34/47.
Basic Operations and Properties
- Square of 34/47: 0.52331371661385
- Cube of 34/47: 0.37856736946534
- Square root of |34/47|: 0.85053174856624
- Reciprocal of 34/47: 1.3823529411765
- Double of 34/47: 1.4468085106383
- Half of 34/47: 0.36170212765957
- Absolute value of 34/47: 0.72340425531915
Trigonometric Functions
- Sine of 34/47: 0.66194018489481
- Cosine of 34/47: 0.74955666338271
- Tangent of 34/47: 0.88310893256222
Exponential and Logarithmic Functions
- e^34/47: 2.0614389437153
- Natural log of 34/47: -0.3237870770939
Floor and Ceiling Functions
- Floor of 34/47: 0
- Ceiling of 34/47: 1
Interesting Properties and Relationships
- The sum of 34/47 and its additive inverse (-34/47) is always 0.
- The product of 34/47 and its additive inverse is: -1156
- The average of 34/47 and its additive inverse is always 0.
- The distance between 34/47 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34/47 = 0
The solution to this equation is x = -34/47, which is the additive inverse of 34/47.
Graphical Representation
On a coordinate plane:
- The point (34/47, 0) is reflected across the y-axis to (-34/47, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34/47 and Its Additive Inverse
Consider the alternating series: 34/47 + (-34/47) + 34/47 + (-34/47) + ...
The sum of this series oscillates between 0 and 34/47, never converging unless 34/47 is 0.
In Number Theory
For integer values:
- If 34/47 is even, its additive inverse is also even.
- If 34/47 is odd, its additive inverse is also odd.
- The sum of the digits of 34/47 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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