31/45 Additive Inverse :
The additive inverse of 31/45 is -31/45.
This means that when we add 31/45 and -31/45, the result is zero:
31/45 + (-31/45) = 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: 31/45
- Additive inverse: -31/45
To verify: 31/45 + (-31/45) = 0
Extended Mathematical Exploration of 31/45
Let's explore various mathematical operations and concepts related to 31/45 and its additive inverse -31/45.
Basic Operations and Properties
- Square of 31/45: 0.47456790123457
- Cube of 31/45: 0.32692455418381
- Square root of |31/45|: 0.82999330653258
- Reciprocal of 31/45: 1.4516129032258
- Double of 31/45: 1.3777777777778
- Half of 31/45: 0.34444444444444
- Absolute value of 31/45: 0.68888888888889
Trigonometric Functions
- Sine of 31/45: 0.63567984945748
- Cosine of 31/45: 0.77195280230964
- Tangent of 31/45: 0.82346983851288
Exponential and Logarithmic Functions
- e^31/45: 1.9915015239946
- Natural log of 31/45: -0.37267528528517
Floor and Ceiling Functions
- Floor of 31/45: 0
- Ceiling of 31/45: 1
Interesting Properties and Relationships
- The sum of 31/45 and its additive inverse (-31/45) is always 0.
- The product of 31/45 and its additive inverse is: -961
- The average of 31/45 and its additive inverse is always 0.
- The distance between 31/45 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/45 = 0
The solution to this equation is x = -31/45, which is the additive inverse of 31/45.
Graphical Representation
On a coordinate plane:
- The point (31/45, 0) is reflected across the y-axis to (-31/45, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/45 and Its Additive Inverse
Consider the alternating series: 31/45 + (-31/45) + 31/45 + (-31/45) + ...
The sum of this series oscillates between 0 and 31/45, never converging unless 31/45 is 0.
In Number Theory
For integer values:
- If 31/45 is even, its additive inverse is also even.
- If 31/45 is odd, its additive inverse is also odd.
- The sum of the digits of 31/45 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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