7/13 Additive Inverse :
The additive inverse of 7/13 is -7/13.
This means that when we add 7/13 and -7/13, the result is zero:
7/13 + (-7/13) = 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: 7/13
- Additive inverse: -7/13
To verify: 7/13 + (-7/13) = 0
Extended Mathematical Exploration of 7/13
Let's explore various mathematical operations and concepts related to 7/13 and its additive inverse -7/13.
Basic Operations and Properties
- Square of 7/13: 0.28994082840237
- Cube of 7/13: 0.15612198452435
- Square root of |7/13|: 0.73379938570534
- Reciprocal of 7/13: 1.8571428571429
- Double of 7/13: 1.0769230769231
- Half of 7/13: 0.26923076923077
- Absolute value of 7/13: 0.53846153846154
Trigonometric Functions
- Sine of 7/13: 0.51281583191132
- Cosine of 7/13: 0.85849864446084
- Tangent of 7/13: 0.59734029310365
Exponential and Logarithmic Functions
- e^7/13: 1.713368881364
- Natural log of 7/13: -0.61903920840622
Floor and Ceiling Functions
- Floor of 7/13: 0
- Ceiling of 7/13: 1
Interesting Properties and Relationships
- The sum of 7/13 and its additive inverse (-7/13) is always 0.
- The product of 7/13 and its additive inverse is: -49
- The average of 7/13 and its additive inverse is always 0.
- The distance between 7/13 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7/13 = 0
The solution to this equation is x = -7/13, which is the additive inverse of 7/13.
Graphical Representation
On a coordinate plane:
- The point (7/13, 0) is reflected across the y-axis to (-7/13, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7/13 and Its Additive Inverse
Consider the alternating series: 7/13 + (-7/13) + 7/13 + (-7/13) + ...
The sum of this series oscillates between 0 and 7/13, never converging unless 7/13 is 0.
In Number Theory
For integer values:
- If 7/13 is even, its additive inverse is also even.
- If 7/13 is odd, its additive inverse is also odd.
- The sum of the digits of 7/13 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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