31/40 Additive Inverse :
The additive inverse of 31/40 is -31/40.
This means that when we add 31/40 and -31/40, the result is zero:
31/40 + (-31/40) = 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: 31/40
- Additive inverse: -31/40
To verify: 31/40 + (-31/40) = 0
Extended Mathematical Exploration of 31/40
Let's explore various mathematical operations and concepts related to 31/40 and its additive inverse -31/40.
Basic Operations and Properties
- Square of 31/40: 0.600625
- Cube of 31/40: 0.465484375
- Square root of |31/40|: 0.88034084308295
- Reciprocal of 31/40: 1.2903225806452
- Double of 31/40: 1.55
- Half of 31/40: 0.3875
- Absolute value of 31/40: 0.775
Trigonometric Functions
- Sine of 31/40: 0.6997160753466
- Cosine of 31/40: 0.71442103405593
- Tangent of 31/40: 0.97941695721661
Exponential and Logarithmic Functions
- e^31/40: 2.1705921271834
- Natural log of 31/40: -0.25489224962879
Floor and Ceiling Functions
- Floor of 31/40: 0
- Ceiling of 31/40: 1
Interesting Properties and Relationships
- The sum of 31/40 and its additive inverse (-31/40) is always 0.
- The product of 31/40 and its additive inverse is: -961
- The average of 31/40 and its additive inverse is always 0.
- The distance between 31/40 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/40 = 0
The solution to this equation is x = -31/40, which is the additive inverse of 31/40.
Graphical Representation
On a coordinate plane:
- The point (31/40, 0) is reflected across the y-axis to (-31/40, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/40 and Its Additive Inverse
Consider the alternating series: 31/40 + (-31/40) + 31/40 + (-31/40) + ...
The sum of this series oscillates between 0 and 31/40, never converging unless 31/40 is 0.
In Number Theory
For integer values:
- If 31/40 is even, its additive inverse is also even.
- If 31/40 is odd, its additive inverse is also odd.
- The sum of the digits of 31/40 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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