47/48 Additive Inverse :
The additive inverse of 47/48 is -47/48.
This means that when we add 47/48 and -47/48, the result is zero:
47/48 + (-47/48) = 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: 47/48
- Additive inverse: -47/48
To verify: 47/48 + (-47/48) = 0
Extended Mathematical Exploration of 47/48
Let's explore various mathematical operations and concepts related to 47/48 and its additive inverse -47/48.
Basic Operations and Properties
- Square of 47/48: 0.95876736111111
- Cube of 47/48: 0.93879304108796
- Square root of |47/48|: 0.98952850725316
- Reciprocal of 47/48: 1.0212765957447
- Double of 47/48: 1.9583333333333
- Half of 47/48: 0.48958333333333
- Absolute value of 47/48: 0.97916666666667
Trigonometric Functions
- Sine of 47/48: 0.83003289672293
- Cosine of 47/48: 0.5577144344176
- Tangent of 47/48: 1.4882758011987
Exponential and Logarithmic Functions
- e^47/48: 2.6622367866293
- Natural log of 47/48: -0.021053409197832
Floor and Ceiling Functions
- Floor of 47/48: 0
- Ceiling of 47/48: 1
Interesting Properties and Relationships
- The sum of 47/48 and its additive inverse (-47/48) is always 0.
- The product of 47/48 and its additive inverse is: -2209
- The average of 47/48 and its additive inverse is always 0.
- The distance between 47/48 and its additive inverse on a number line is: 94
Applications in Algebra
Consider the equation: x + 47/48 = 0
The solution to this equation is x = -47/48, which is the additive inverse of 47/48.
Graphical Representation
On a coordinate plane:
- The point (47/48, 0) is reflected across the y-axis to (-47/48, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 47/48 and Its Additive Inverse
Consider the alternating series: 47/48 + (-47/48) + 47/48 + (-47/48) + ...
The sum of this series oscillates between 0 and 47/48, never converging unless 47/48 is 0.
In Number Theory
For integer values:
- If 47/48 is even, its additive inverse is also even.
- If 47/48 is odd, its additive inverse is also odd.
- The sum of the digits of 47/48 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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