31/42 Additive Inverse :
The additive inverse of 31/42 is -31/42.
This means that when we add 31/42 and -31/42, the result is zero:
31/42 + (-31/42) = 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: 31/42
- Additive inverse: -31/42
To verify: 31/42 + (-31/42) = 0
Extended Mathematical Exploration of 31/42
Let's explore various mathematical operations and concepts related to 31/42 and its additive inverse -31/42.
Basic Operations and Properties
- Square of 31/42: 0.54478458049887
- Cube of 31/42: 0.40210290465393
- Square root of |31/42|: 0.85912469298422
- Reciprocal of 31/42: 1.3548387096774
- Double of 31/42: 1.4761904761905
- Half of 31/42: 0.36904761904762
- Absolute value of 31/42: 0.73809523809524
Trigonometric Functions
- Sine of 31/42: 0.67288008250251
- Cosine of 31/42: 0.73975157625477
- Tangent of 31/42: 0.9096027694989
Exponential and Logarithmic Functions
- e^31/42: 2.0919470561092
- Natural log of 31/42: -0.30368241379822
Floor and Ceiling Functions
- Floor of 31/42: 0
- Ceiling of 31/42: 1
Interesting Properties and Relationships
- The sum of 31/42 and its additive inverse (-31/42) is always 0.
- The product of 31/42 and its additive inverse is: -961
- The average of 31/42 and its additive inverse is always 0.
- The distance between 31/42 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/42 = 0
The solution to this equation is x = -31/42, which is the additive inverse of 31/42.
Graphical Representation
On a coordinate plane:
- The point (31/42, 0) is reflected across the y-axis to (-31/42, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/42 and Its Additive Inverse
Consider the alternating series: 31/42 + (-31/42) + 31/42 + (-31/42) + ...
The sum of this series oscillates between 0 and 31/42, never converging unless 31/42 is 0.
In Number Theory
For integer values:
- If 31/42 is even, its additive inverse is also even.
- If 31/42 is odd, its additive inverse is also odd.
- The sum of the digits of 31/42 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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