45/47 Additive Inverse :
The additive inverse of 45/47 is -45/47.
This means that when we add 45/47 and -45/47, the result is zero:
45/47 + (-45/47) = 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: 45/47
- Additive inverse: -45/47
To verify: 45/47 + (-45/47) = 0
Extended Mathematical Exploration of 45/47
Let's explore various mathematical operations and concepts related to 45/47 and its additive inverse -45/47.
Basic Operations and Properties
- Square of 45/47: 0.91670439112721
- Cube of 45/47: 0.87769569363243
- Square root of |45/47|: 0.97849210958016
- Reciprocal of 45/47: 1.0444444444444
- Double of 45/47: 1.9148936170213
- Half of 45/47: 0.47872340425532
- Absolute value of 45/47: 0.95744680851064
Trigonometric Functions
- Sine of 45/47: 0.81772459347836
- Cosine of 45/47: 0.57560966741417
- Tangent of 45/47: 1.4206234533062
Exponential and Logarithmic Functions
- e^45/47: 2.6050368175205
- Natural log of 45/47: -0.043485111939739
Floor and Ceiling Functions
- Floor of 45/47: 0
- Ceiling of 45/47: 1
Interesting Properties and Relationships
- The sum of 45/47 and its additive inverse (-45/47) is always 0.
- The product of 45/47 and its additive inverse is: -2025
- The average of 45/47 and its additive inverse is always 0.
- The distance between 45/47 and its additive inverse on a number line is: 90
Applications in Algebra
Consider the equation: x + 45/47 = 0
The solution to this equation is x = -45/47, which is the additive inverse of 45/47.
Graphical Representation
On a coordinate plane:
- The point (45/47, 0) is reflected across the y-axis to (-45/47, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 45/47 and Its Additive Inverse
Consider the alternating series: 45/47 + (-45/47) + 45/47 + (-45/47) + ...
The sum of this series oscillates between 0 and 45/47, never converging unless 45/47 is 0.
In Number Theory
For integer values:
- If 45/47 is even, its additive inverse is also even.
- If 45/47 is odd, its additive inverse is also odd.
- The sum of the digits of 45/47 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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