31/38 Additive Inverse :
The additive inverse of 31/38 is -31/38.
This means that when we add 31/38 and -31/38, the result is zero:
31/38 + (-31/38) = 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: 31/38
- Additive inverse: -31/38
To verify: 31/38 + (-31/38) = 0
Extended Mathematical Exploration of 31/38
Let's explore various mathematical operations and concepts related to 31/38 and its additive inverse -31/38.
Basic Operations and Properties
- Square of 31/38: 0.66551246537396
- Cube of 31/38: 0.54291806385771
- Square root of |31/38|: 0.9032106474595
- Reciprocal of 31/38: 1.2258064516129
- Double of 31/38: 1.6315789473684
- Half of 31/38: 0.40789473684211
- Absolute value of 31/38: 0.81578947368421
Trigonometric Functions
- Sine of 31/38: 0.72826684680649
- Cosine of 31/38: 0.68529365956686
- Tangent of 31/38: 1.062707697116
Exponential and Logarithmic Functions
- e^31/38: 2.2609599363131
- Natural log of 31/38: -0.20359895524124
Floor and Ceiling Functions
- Floor of 31/38: 0
- Ceiling of 31/38: 1
Interesting Properties and Relationships
- The sum of 31/38 and its additive inverse (-31/38) is always 0.
- The product of 31/38 and its additive inverse is: -961
- The average of 31/38 and its additive inverse is always 0.
- The distance between 31/38 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/38 = 0
The solution to this equation is x = -31/38, which is the additive inverse of 31/38.
Graphical Representation
On a coordinate plane:
- The point (31/38, 0) is reflected across the y-axis to (-31/38, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/38 and Its Additive Inverse
Consider the alternating series: 31/38 + (-31/38) + 31/38 + (-31/38) + ...
The sum of this series oscillates between 0 and 31/38, never converging unless 31/38 is 0.
In Number Theory
For integer values:
- If 31/38 is even, its additive inverse is also even.
- If 31/38 is odd, its additive inverse is also odd.
- The sum of the digits of 31/38 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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