48/63 Additive Inverse :
The additive inverse of 48/63 is -48/63.
This means that when we add 48/63 and -48/63, the result is zero:
48/63 + (-48/63) = 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: 48/63
- Additive inverse: -48/63
To verify: 48/63 + (-48/63) = 0
Extended Mathematical Exploration of 48/63
Let's explore various mathematical operations and concepts related to 48/63 and its additive inverse -48/63.
Basic Operations and Properties
- Square of 48/63: 0.58049886621315
- Cube of 48/63: 0.44228485044812
- Square root of |48/63|: 0.87287156094397
- Reciprocal of 48/63: 1.3125
- Double of 48/63: 1.5238095238095
- Half of 48/63: 0.38095238095238
- Absolute value of 48/63: 0.76190476190476
Trigonometric Functions
- Sine of 48/63: 0.69030083455242
- Cosine of 48/63: 0.72352246531551
- Tangent of 48/63: 0.95408348412705
Exponential and Logarithmic Functions
- e^48/63: 2.1423530090066
- Natural log of 48/63: -0.27193371548364
Floor and Ceiling Functions
- Floor of 48/63: 0
- Ceiling of 48/63: 1
Interesting Properties and Relationships
- The sum of 48/63 and its additive inverse (-48/63) is always 0.
- The product of 48/63 and its additive inverse is: -2304
- The average of 48/63 and its additive inverse is always 0.
- The distance between 48/63 and its additive inverse on a number line is: 96
Applications in Algebra
Consider the equation: x + 48/63 = 0
The solution to this equation is x = -48/63, which is the additive inverse of 48/63.
Graphical Representation
On a coordinate plane:
- The point (48/63, 0) is reflected across the y-axis to (-48/63, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 48/63 and Its Additive Inverse
Consider the alternating series: 48/63 + (-48/63) + 48/63 + (-48/63) + ...
The sum of this series oscillates between 0 and 48/63, never converging unless 48/63 is 0.
In Number Theory
For integer values:
- If 48/63 is even, its additive inverse is also even.
- If 48/63 is odd, its additive inverse is also odd.
- The sum of the digits of 48/63 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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