13/15 Additive Inverse :
The additive inverse of 13/15 is -13/15.
This means that when we add 13/15 and -13/15, the result is zero:
13/15 + (-13/15) = 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: 13/15
- Additive inverse: -13/15
To verify: 13/15 + (-13/15) = 0
Extended Mathematical Exploration of 13/15
Let's explore various mathematical operations and concepts related to 13/15 and its additive inverse -13/15.
Basic Operations and Properties
- Square of 13/15: 0.75111111111111
- Cube of 13/15: 0.65096296296296
- Square root of |13/15|: 0.93094933625126
- Reciprocal of 13/15: 1.1538461538462
- Double of 13/15: 1.7333333333333
- Half of 13/15: 0.43333333333333
- Absolute value of 13/15: 0.86666666666667
Trigonometric Functions
- Sine of 13/15: 0.76217527291384
- Cosine of 13/15: 0.64737072327895
- Tangent of 13/15: 1.1773397305541
Exponential and Logarithmic Functions
- e^13/15: 2.3789677299066
- Natural log of 13/15: -0.14310084364067
Floor and Ceiling Functions
- Floor of 13/15: 0
- Ceiling of 13/15: 1
Interesting Properties and Relationships
- The sum of 13/15 and its additive inverse (-13/15) is always 0.
- The product of 13/15 and its additive inverse is: -169
- The average of 13/15 and its additive inverse is always 0.
- The distance between 13/15 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13/15 = 0
The solution to this equation is x = -13/15, which is the additive inverse of 13/15.
Graphical Representation
On a coordinate plane:
- The point (13/15, 0) is reflected across the y-axis to (-13/15, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13/15 and Its Additive Inverse
Consider the alternating series: 13/15 + (-13/15) + 13/15 + (-13/15) + ...
The sum of this series oscillates between 0 and 13/15, never converging unless 13/15 is 0.
In Number Theory
For integer values:
- If 13/15 is even, its additive inverse is also even.
- If 13/15 is odd, its additive inverse is also odd.
- The sum of the digits of 13/15 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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