48/49 Additive Inverse :
The additive inverse of 48/49 is -48/49.
This means that when we add 48/49 and -48/49, the result is zero:
48/49 + (-48/49) = 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: 48/49
- Additive inverse: -48/49
To verify: 48/49 + (-48/49) = 0
Extended Mathematical Exploration of 48/49
Let's explore various mathematical operations and concepts related to 48/49 and its additive inverse -48/49.
Basic Operations and Properties
- Square of 48/49: 0.95960016659725
- Cube of 48/49: 0.94001648972792
- Square root of |48/49|: 0.98974331861079
- Reciprocal of 48/49: 1.0208333333333
- Double of 48/49: 1.9591836734694
- Half of 48/49: 0.48979591836735
- Absolute value of 48/49: 0.97959183673469
Trigonometric Functions
- Sine of 48/49: 0.83026994517746
- Cosine of 48/49: 0.55736147887616
- Tangent of 48/49: 1.4896435735953
Exponential and Logarithmic Functions
- e^48/49: 2.6633689306848
- Natural log of 48/49: -0.020619287202736
Floor and Ceiling Functions
- Floor of 48/49: 0
- Ceiling of 48/49: 1
Interesting Properties and Relationships
- The sum of 48/49 and its additive inverse (-48/49) is always 0.
- The product of 48/49 and its additive inverse is: -2304
- The average of 48/49 and its additive inverse is always 0.
- The distance between 48/49 and its additive inverse on a number line is: 96
Applications in Algebra
Consider the equation: x + 48/49 = 0
The solution to this equation is x = -48/49, which is the additive inverse of 48/49.
Graphical Representation
On a coordinate plane:
- The point (48/49, 0) is reflected across the y-axis to (-48/49, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 48/49 and Its Additive Inverse
Consider the alternating series: 48/49 + (-48/49) + 48/49 + (-48/49) + ...
The sum of this series oscillates between 0 and 48/49, never converging unless 48/49 is 0.
In Number Theory
For integer values:
- If 48/49 is even, its additive inverse is also even.
- If 48/49 is odd, its additive inverse is also odd.
- The sum of the digits of 48/49 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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