42/47 Additive Inverse :
The additive inverse of 42/47 is -42/47.
This means that when we add 42/47 and -42/47, the result is zero:
42/47 + (-42/47) = 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: 42/47
- Additive inverse: -42/47
To verify: 42/47 + (-42/47) = 0
Extended Mathematical Exploration of 42/47
Let's explore various mathematical operations and concepts related to 42/47 and its additive inverse -42/47.
Basic Operations and Properties
- Square of 42/47: 0.79855138071526
- Cube of 42/47: 0.71359910617108
- Square root of |42/47|: 0.94531318687332
- Reciprocal of 42/47: 1.1190476190476
- Double of 42/47: 1.7872340425532
- Half of 42/47: 0.4468085106383
- Absolute value of 42/47: 0.8936170212766
Trigonometric Functions
- Sine of 42/47: 0.77934325610637
- Cosine of 42/47: 0.62659723041322
- Tangent of 42/47: 1.2437706684283
Exponential and Logarithmic Functions
- e^42/47: 2.443953515482
- Natural log of 42/47: -0.11247798342669
Floor and Ceiling Functions
- Floor of 42/47: 0
- Ceiling of 42/47: 1
Interesting Properties and Relationships
- The sum of 42/47 and its additive inverse (-42/47) is always 0.
- The product of 42/47 and its additive inverse is: -1764
- The average of 42/47 and its additive inverse is always 0.
- The distance between 42/47 and its additive inverse on a number line is: 84
Applications in Algebra
Consider the equation: x + 42/47 = 0
The solution to this equation is x = -42/47, which is the additive inverse of 42/47.
Graphical Representation
On a coordinate plane:
- The point (42/47, 0) is reflected across the y-axis to (-42/47, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 42/47 and Its Additive Inverse
Consider the alternating series: 42/47 + (-42/47) + 42/47 + (-42/47) + ...
The sum of this series oscillates between 0 and 42/47, never converging unless 42/47 is 0.
In Number Theory
For integer values:
- If 42/47 is even, its additive inverse is also even.
- If 42/47 is odd, its additive inverse is also odd.
- The sum of the digits of 42/47 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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