45/48 Additive Inverse :
The additive inverse of 45/48 is -45/48.
This means that when we add 45/48 and -45/48, the result is zero:
45/48 + (-45/48) = 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: 45/48
- Additive inverse: -45/48
To verify: 45/48 + (-45/48) = 0
Extended Mathematical Exploration of 45/48
Let's explore various mathematical operations and concepts related to 45/48 and its additive inverse -45/48.
Basic Operations and Properties
- Square of 45/48: 0.87890625
- Cube of 45/48: 0.823974609375
- Square root of |45/48|: 0.96824583655185
- Reciprocal of 45/48: 1.0666666666667
- Double of 45/48: 1.875
- Half of 45/48: 0.46875
- Absolute value of 45/48: 0.9375
Trigonometric Functions
- Sine of 45/48: 0.80608110826069
- Cosine of 45/48: 0.59180507509248
- Tangent of 45/48: 1.3620719763762
Exponential and Logarithmic Functions
- e^45/48: 2.5535894580629
- Natural log of 45/48: -0.064538521137571
Floor and Ceiling Functions
- Floor of 45/48: 0
- Ceiling of 45/48: 1
Interesting Properties and Relationships
- The sum of 45/48 and its additive inverse (-45/48) is always 0.
- The product of 45/48 and its additive inverse is: -2025
- The average of 45/48 and its additive inverse is always 0.
- The distance between 45/48 and its additive inverse on a number line is: 90
Applications in Algebra
Consider the equation: x + 45/48 = 0
The solution to this equation is x = -45/48, which is the additive inverse of 45/48.
Graphical Representation
On a coordinate plane:
- The point (45/48, 0) is reflected across the y-axis to (-45/48, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 45/48 and Its Additive Inverse
Consider the alternating series: 45/48 + (-45/48) + 45/48 + (-45/48) + ...
The sum of this series oscillates between 0 and 45/48, never converging unless 45/48 is 0.
In Number Theory
For integer values:
- If 45/48 is even, its additive inverse is also even.
- If 45/48 is odd, its additive inverse is also odd.
- The sum of the digits of 45/48 and its additive inverse may or may not be the same.
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