31/33 Additive Inverse :
The additive inverse of 31/33 is -31/33.
This means that when we add 31/33 and -31/33, the result is zero:
31/33 + (-31/33) = 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: 31/33
- Additive inverse: -31/33
To verify: 31/33 + (-31/33) = 0
Extended Mathematical Exploration of 31/33
Let's explore various mathematical operations and concepts related to 31/33 and its additive inverse -31/33.
Basic Operations and Properties
- Square of 31/33: 0.88246097337006
- Cube of 31/33: 0.82897849013552
- Square root of |31/33|: 0.96922336919512
- Reciprocal of 31/33: 1.0645161290323
- Double of 31/33: 1.8787878787879
- Half of 31/33: 0.46969696969697
- Absolute value of 31/33: 0.93939393939394
Trigonometric Functions
- Sine of 31/33: 0.80720050482724
- Cosine of 31/33: 0.59027734583554
- Tangent of 31/33: 1.3674936206211
Exponential and Logarithmic Functions
- e^31/33: 2.5584303844971
- Natural log of 31/33: -0.062520356981334
Floor and Ceiling Functions
- Floor of 31/33: 0
- Ceiling of 31/33: 1
Interesting Properties and Relationships
- The sum of 31/33 and its additive inverse (-31/33) is always 0.
- The product of 31/33 and its additive inverse is: -961
- The average of 31/33 and its additive inverse is always 0.
- The distance between 31/33 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/33 = 0
The solution to this equation is x = -31/33, which is the additive inverse of 31/33.
Graphical Representation
On a coordinate plane:
- The point (31/33, 0) is reflected across the y-axis to (-31/33, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/33 and Its Additive Inverse
Consider the alternating series: 31/33 + (-31/33) + 31/33 + (-31/33) + ...
The sum of this series oscillates between 0 and 31/33, never converging unless 31/33 is 0.
In Number Theory
For integer values:
- If 31/33 is even, its additive inverse is also even.
- If 31/33 is odd, its additive inverse is also odd.
- The sum of the digits of 31/33 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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