31/34 Additive Inverse :
The additive inverse of 31/34 is -31/34.
This means that when we add 31/34 and -31/34, the result is zero:
31/34 + (-31/34) = 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: 31/34
- Additive inverse: -31/34
To verify: 31/34 + (-31/34) = 0
Extended Mathematical Exploration of 31/34
Let's explore various mathematical operations and concepts related to 31/34 and its additive inverse -31/34.
Basic Operations and Properties
- Square of 31/34: 0.83131487889273
- Cube of 31/34: 0.75796356604926
- Square root of |31/34|: 0.95486371063223
- Reciprocal of 31/34: 1.0967741935484
- Double of 31/34: 1.8235294117647
- Half of 31/34: 0.45588235294118
- Absolute value of 31/34: 0.91176470588235
Trigonometric Functions
- Sine of 31/34: 0.79058559053143
- Cosine of 31/34: 0.61235155265915
- Tangent of 31/34: 1.2910648909083
Exponential and Logarithmic Functions
- e^31/34: 2.4887105025719
- Natural log of 31/34: -0.092373320131015
Floor and Ceiling Functions
- Floor of 31/34: 0
- Ceiling of 31/34: 1
Interesting Properties and Relationships
- The sum of 31/34 and its additive inverse (-31/34) is always 0.
- The product of 31/34 and its additive inverse is: -961
- The average of 31/34 and its additive inverse is always 0.
- The distance between 31/34 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/34 = 0
The solution to this equation is x = -31/34, which is the additive inverse of 31/34.
Graphical Representation
On a coordinate plane:
- The point (31/34, 0) is reflected across the y-axis to (-31/34, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/34 and Its Additive Inverse
Consider the alternating series: 31/34 + (-31/34) + 31/34 + (-31/34) + ...
The sum of this series oscillates between 0 and 31/34, never converging unless 31/34 is 0.
In Number Theory
For integer values:
- If 31/34 is even, its additive inverse is also even.
- If 31/34 is odd, its additive inverse is also odd.
- The sum of the digits of 31/34 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: