38/47 Additive Inverse :
The additive inverse of 38/47 is -38/47.
This means that when we add 38/47 and -38/47, the result is zero:
38/47 + (-38/47) = 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: 38/47
- Additive inverse: -38/47
To verify: 38/47 + (-38/47) = 0
Extended Mathematical Exploration of 38/47
Let's explore various mathematical operations and concepts related to 38/47 and its additive inverse -38/47.
Basic Operations and Properties
- Square of 38/47: 0.65368945224083
- Cube of 38/47: 0.52851487627982
- Square root of |38/47|: 0.89917219613257
- Reciprocal of 38/47: 1.2368421052632
- Double of 38/47: 1.6170212765957
- Half of 38/47: 0.40425531914894
- Absolute value of 38/47: 0.80851063829787
Trigonometric Functions
- Sine of 38/47: 0.72325945888394
- Cosine of 38/47: 0.69057639340981
- Tangent of 38/47: 1.047327226627
Exponential and Logarithmic Functions
- e^38/47: 2.2445625305267
- Natural log of 38/47: -0.21256144198367
Floor and Ceiling Functions
- Floor of 38/47: 0
- Ceiling of 38/47: 1
Interesting Properties and Relationships
- The sum of 38/47 and its additive inverse (-38/47) is always 0.
- The product of 38/47 and its additive inverse is: -1444
- The average of 38/47 and its additive inverse is always 0.
- The distance between 38/47 and its additive inverse on a number line is: 76
Applications in Algebra
Consider the equation: x + 38/47 = 0
The solution to this equation is x = -38/47, which is the additive inverse of 38/47.
Graphical Representation
On a coordinate plane:
- The point (38/47, 0) is reflected across the y-axis to (-38/47, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 38/47 and Its Additive Inverse
Consider the alternating series: 38/47 + (-38/47) + 38/47 + (-38/47) + ...
The sum of this series oscillates between 0 and 38/47, never converging unless 38/47 is 0.
In Number Theory
For integer values:
- If 38/47 is even, its additive inverse is also even.
- If 38/47 is odd, its additive inverse is also odd.
- The sum of the digits of 38/47 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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