10/17 Additive Inverse :
The additive inverse of 10/17 is -10/17.
This means that when we add 10/17 and -10/17, the result is zero:
10/17 + (-10/17) = 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: 10/17
- Additive inverse: -10/17
To verify: 10/17 + (-10/17) = 0
Extended Mathematical Exploration of 10/17
Let's explore various mathematical operations and concepts related to 10/17 and its additive inverse -10/17.
Basic Operations and Properties
- Square of 10/17: 0.34602076124567
- Cube of 10/17: 0.20354162426216
- Square root of |10/17|: 0.76696498884737
- Reciprocal of 10/17: 1.7
- Double of 10/17: 1.1764705882353
- Half of 10/17: 0.29411764705882
- Absolute value of 10/17: 0.58823529411765
Trigonometric Functions
- Sine of 10/17: 0.55489379146371
- Cosine of 10/17: 0.83192119830849
- Tangent of 10/17: 0.66700282742158
Exponential and Logarithmic Functions
- e^10/17: 1.8008077137564
- Natural log of 10/17: -0.53062825106217
Floor and Ceiling Functions
- Floor of 10/17: 0
- Ceiling of 10/17: 1
Interesting Properties and Relationships
- The sum of 10/17 and its additive inverse (-10/17) is always 0.
- The product of 10/17 and its additive inverse is: -100
- The average of 10/17 and its additive inverse is always 0.
- The distance between 10/17 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/17 = 0
The solution to this equation is x = -10/17, which is the additive inverse of 10/17.
Graphical Representation
On a coordinate plane:
- The point (10/17, 0) is reflected across the y-axis to (-10/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/17 and Its Additive Inverse
Consider the alternating series: 10/17 + (-10/17) + 10/17 + (-10/17) + ...
The sum of this series oscillates between 0 and 10/17, never converging unless 10/17 is 0.
In Number Theory
For integer values:
- If 10/17 is even, its additive inverse is also even.
- If 10/17 is odd, its additive inverse is also odd.
- The sum of the digits of 10/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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