7/17 Additive Inverse :
The additive inverse of 7/17 is -7/17.
This means that when we add 7/17 and -7/17, the result is zero:
7/17 + (-7/17) = 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: 7/17
- Additive inverse: -7/17
To verify: 7/17 + (-7/17) = 0
Extended Mathematical Exploration of 7/17
Let's explore various mathematical operations and concepts related to 7/17 and its additive inverse -7/17.
Basic Operations and Properties
- Square of 7/17: 0.16955017301038
- Cube of 7/17: 0.069814777121921
- Square root of |7/17|: 0.64168894791975
- Reciprocal of 7/17: 2.4285714285714
- Double of 7/17: 0.82352941176471
- Half of 7/17: 0.20588235294118
- Absolute value of 7/17: 0.41176470588235
Trigonometric Functions
- Sine of 7/17: 0.40022715498345
- Cosine of 7/17: 0.91641596691342
- Tangent of 7/17: 0.43673088360895
Exponential and Logarithmic Functions
- e^7/17: 1.5094792229587
- Natural log of 7/17: -0.8873031950009
Floor and Ceiling Functions
- Floor of 7/17: 0
- Ceiling of 7/17: 1
Interesting Properties and Relationships
- The sum of 7/17 and its additive inverse (-7/17) is always 0.
- The product of 7/17 and its additive inverse is: -49
- The average of 7/17 and its additive inverse is always 0.
- The distance between 7/17 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7/17 = 0
The solution to this equation is x = -7/17, which is the additive inverse of 7/17.
Graphical Representation
On a coordinate plane:
- The point (7/17, 0) is reflected across the y-axis to (-7/17, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7/17 and Its Additive Inverse
Consider the alternating series: 7/17 + (-7/17) + 7/17 + (-7/17) + ...
The sum of this series oscillates between 0 and 7/17, never converging unless 7/17 is 0.
In Number Theory
For integer values:
- If 7/17 is even, its additive inverse is also even.
- If 7/17 is odd, its additive inverse is also odd.
- The sum of the digits of 7/17 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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