13/17 Additive Inverse :
The additive inverse of 13/17 is -13/17.
This means that when we add 13/17 and -13/17, the result is zero:
13/17 + (-13/17) = 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: 13/17
- Additive inverse: -13/17
To verify: 13/17 + (-13/17) = 0
Extended Mathematical Exploration of 13/17
Let's explore various mathematical operations and concepts related to 13/17 and its additive inverse -13/17.
Basic Operations and Properties
- Square of 13/17: 0.58477508650519
- Cube of 13/17: 0.44718094850397
- Square root of |13/17|: 0.87447463219521
- Reciprocal of 13/17: 1.3076923076923
- Double of 13/17: 1.5294117647059
- Half of 13/17: 0.38235294117647
- Absolute value of 13/17: 0.76470588235294
Trigonometric Functions
- Sine of 13/17: 0.69232479733084
- Cosine of 13/17: 0.72158601358453
- Tangent of 13/17: 0.95944874803167
Exponential and Logarithmic Functions
- e^13/17: 2.1483624104267
- Natural log of 13/17: -0.26826398659468
Floor and Ceiling Functions
- Floor of 13/17: 0
- Ceiling of 13/17: 1
Interesting Properties and Relationships
- The sum of 13/17 and its additive inverse (-13/17) is always 0.
- The product of 13/17 and its additive inverse is: -169
- The average of 13/17 and its additive inverse is always 0.
- The distance between 13/17 and its additive inverse on a number line is: 26
Applications in Algebra
Consider the equation: x + 13/17 = 0
The solution to this equation is x = -13/17, which is the additive inverse of 13/17.
Graphical Representation
On a coordinate plane:
- The point (13/17, 0) is reflected across the y-axis to (-13/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13/17 and Its Additive Inverse
Consider the alternating series: 13/17 + (-13/17) + 13/17 + (-13/17) + ...
The sum of this series oscillates between 0 and 13/17, never converging unless 13/17 is 0.
In Number Theory
For integer values:
- If 13/17 is even, its additive inverse is also even.
- If 13/17 is odd, its additive inverse is also odd.
- The sum of the digits of 13/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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