31/43 Additive Inverse :
The additive inverse of 31/43 is -31/43.
This means that when we add 31/43 and -31/43, the result is zero:
31/43 + (-31/43) = 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: 31/43
- Additive inverse: -31/43
To verify: 31/43 + (-31/43) = 0
Extended Mathematical Exploration of 31/43
Let's explore various mathematical operations and concepts related to 31/43 and its additive inverse -31/43.
Basic Operations and Properties
- Square of 31/43: 0.51974040021633
- Cube of 31/43: 0.37469656759782
- Square root of |31/43|: 0.8490761052804
- Reciprocal of 31/43: 1.3870967741935
- Double of 31/43: 1.4418604651163
- Half of 31/43: 0.36046511627907
- Absolute value of 31/43: 0.72093023255814
Trigonometric Functions
- Sine of 31/43: 0.66008374074374
- Cosine of 31/43: 0.75119202285817
- Tangent of 31/43: 0.87871505641424
Exponential and Logarithmic Functions
- e^31/43: 2.0563452004647
- Natural log of 31/43: -0.32721291120842
Floor and Ceiling Functions
- Floor of 31/43: 0
- Ceiling of 31/43: 1
Interesting Properties and Relationships
- The sum of 31/43 and its additive inverse (-31/43) is always 0.
- The product of 31/43 and its additive inverse is: -961
- The average of 31/43 and its additive inverse is always 0.
- The distance between 31/43 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/43 = 0
The solution to this equation is x = -31/43, which is the additive inverse of 31/43.
Graphical Representation
On a coordinate plane:
- The point (31/43, 0) is reflected across the y-axis to (-31/43, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/43 and Its Additive Inverse
Consider the alternating series: 31/43 + (-31/43) + 31/43 + (-31/43) + ...
The sum of this series oscillates between 0 and 31/43, never converging unless 31/43 is 0.
In Number Theory
For integer values:
- If 31/43 is even, its additive inverse is also even.
- If 31/43 is odd, its additive inverse is also odd.
- The sum of the digits of 31/43 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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