33/47 Additive Inverse :
The additive inverse of 33/47 is -33/47.
This means that when we add 33/47 and -33/47, the result is zero:
33/47 + (-33/47) = 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: 33/47
- Additive inverse: -33/47
To verify: 33/47 + (-33/47) = 0
Extended Mathematical Exploration of 33/47
Let's explore various mathematical operations and concepts related to 33/47 and its additive inverse -33/47.
Basic Operations and Properties
- Square of 33/47: 0.49298325033952
- Cube of 33/47: 0.3461371757703
- Square root of |33/47|: 0.83793058159639
- Reciprocal of 33/47: 1.4242424242424
- Double of 33/47: 1.4042553191489
- Half of 33/47: 0.35106382978723
- Absolute value of 33/47: 0.70212765957447
Trigonometric Functions
- Sine of 33/47: 0.64584355164729
- Cosine of 33/47: 0.76346978119347
- Tangent of 33/47: 0.84593204283435
Exponential and Logarithmic Functions
- e^33/47: 2.0180418489976
- Natural log of 33/47: -0.35364004024358
Floor and Ceiling Functions
- Floor of 33/47: 0
- Ceiling of 33/47: 1
Interesting Properties and Relationships
- The sum of 33/47 and its additive inverse (-33/47) is always 0.
- The product of 33/47 and its additive inverse is: -1089
- The average of 33/47 and its additive inverse is always 0.
- The distance between 33/47 and its additive inverse on a number line is: 66
Applications in Algebra
Consider the equation: x + 33/47 = 0
The solution to this equation is x = -33/47, which is the additive inverse of 33/47.
Graphical Representation
On a coordinate plane:
- The point (33/47, 0) is reflected across the y-axis to (-33/47, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 33/47 and Its Additive Inverse
Consider the alternating series: 33/47 + (-33/47) + 33/47 + (-33/47) + ...
The sum of this series oscillates between 0 and 33/47, never converging unless 33/47 is 0.
In Number Theory
For integer values:
- If 33/47 is even, its additive inverse is also even.
- If 33/47 is odd, its additive inverse is also odd.
- The sum of the digits of 33/47 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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