26/31 Additive Inverse :
The additive inverse of 26/31 is -26/31.
This means that when we add 26/31 and -26/31, the result is zero:
26/31 + (-26/31) = 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: 26/31
- Additive inverse: -26/31
To verify: 26/31 + (-26/31) = 0
Extended Mathematical Exploration of 26/31
Let's explore various mathematical operations and concepts related to 26/31 and its additive inverse -26/31.
Basic Operations and Properties
- Square of 26/31: 0.70343392299688
- Cube of 26/31: 0.58997683864254
- Square root of |26/31|: 0.91581093977925
- Reciprocal of 26/31: 1.1923076923077
- Double of 26/31: 1.6774193548387
- Half of 26/31: 0.41935483870968
- Absolute value of 26/31: 0.83870967741935
Trigonometric Functions
- Sine of 26/31: 0.74378125796379
- Cosine of 26/31: 0.66842309976676
- Tangent of 26/31: 1.1127402063503
Exponential and Logarithmic Functions
- e^26/31: 2.313380043634
- Natural log of 26/31: -0.17589066646366
Floor and Ceiling Functions
- Floor of 26/31: 0
- Ceiling of 26/31: 1
Interesting Properties and Relationships
- The sum of 26/31 and its additive inverse (-26/31) is always 0.
- The product of 26/31 and its additive inverse is: -676
- The average of 26/31 and its additive inverse is always 0.
- The distance between 26/31 and its additive inverse on a number line is: 52
Applications in Algebra
Consider the equation: x + 26/31 = 0
The solution to this equation is x = -26/31, which is the additive inverse of 26/31.
Graphical Representation
On a coordinate plane:
- The point (26/31, 0) is reflected across the y-axis to (-26/31, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 26/31 and Its Additive Inverse
Consider the alternating series: 26/31 + (-26/31) + 26/31 + (-26/31) + ...
The sum of this series oscillates between 0 and 26/31, never converging unless 26/31 is 0.
In Number Theory
For integer values:
- If 26/31 is even, its additive inverse is also even.
- If 26/31 is odd, its additive inverse is also odd.
- The sum of the digits of 26/31 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: