47/49 Additive Inverse :
The additive inverse of 47/49 is -47/49.
This means that when we add 47/49 and -47/49, the result is zero:
47/49 + (-47/49) = 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: 47/49
- Additive inverse: -47/49
To verify: 47/49 + (-47/49) = 0
Extended Mathematical Exploration of 47/49
Let's explore various mathematical operations and concepts related to 47/49 and its additive inverse -47/49.
Basic Operations and Properties
- Square of 47/49: 0.92003331945023
- Cube of 47/49: 0.88248093906451
- Square root of |47/49|: 0.97937922862872
- Reciprocal of 47/49: 1.0425531914894
- Double of 47/49: 1.9183673469388
- Half of 47/49: 0.47959183673469
- Absolute value of 47/49: 0.95918367346939
Trigonometric Functions
- Sine of 47/49: 0.81872311582242
- Cosine of 47/49: 0.57418852271535
- Tangent of 47/49: 1.425878580698
Exponential and Logarithmic Functions
- e^47/49: 2.6095653462681
- Natural log of 47/49: -0.041672696400568
Floor and Ceiling Functions
- Floor of 47/49: 0
- Ceiling of 47/49: 1
Interesting Properties and Relationships
- The sum of 47/49 and its additive inverse (-47/49) is always 0.
- The product of 47/49 and its additive inverse is: -2209
- The average of 47/49 and its additive inverse is always 0.
- The distance between 47/49 and its additive inverse on a number line is: 94
Applications in Algebra
Consider the equation: x + 47/49 = 0
The solution to this equation is x = -47/49, which is the additive inverse of 47/49.
Graphical Representation
On a coordinate plane:
- The point (47/49, 0) is reflected across the y-axis to (-47/49, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 47/49 and Its Additive Inverse
Consider the alternating series: 47/49 + (-47/49) + 47/49 + (-47/49) + ...
The sum of this series oscillates between 0 and 47/49, never converging unless 47/49 is 0.
In Number Theory
For integer values:
- If 47/49 is even, its additive inverse is also even.
- If 47/49 is odd, its additive inverse is also odd.
- The sum of the digits of 47/49 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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