7/14 Additive Inverse :
The additive inverse of 7/14 is -7/14.
This means that when we add 7/14 and -7/14, the result is zero:
7/14 + (-7/14) = 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: 7/14
- Additive inverse: -7/14
To verify: 7/14 + (-7/14) = 0
Extended Mathematical Exploration of 7/14
Let's explore various mathematical operations and concepts related to 7/14 and its additive inverse -7/14.
Basic Operations and Properties
- Square of 7/14: 0.25
- Cube of 7/14: 0.125
- Square root of |7/14|: 0.70710678118655
- Reciprocal of 7/14: 2
- Double of 7/14: 1
- Half of 7/14: 0.25
- Absolute value of 7/14: 0.5
Trigonometric Functions
- Sine of 7/14: 0.4794255386042
- Cosine of 7/14: 0.87758256189037
- Tangent of 7/14: 0.54630248984379
Exponential and Logarithmic Functions
- e^7/14: 1.6487212707001
- Natural log of 7/14: -0.69314718055995
Floor and Ceiling Functions
- Floor of 7/14: 0
- Ceiling of 7/14: 1
Interesting Properties and Relationships
- The sum of 7/14 and its additive inverse (-7/14) is always 0.
- The product of 7/14 and its additive inverse is: -49
- The average of 7/14 and its additive inverse is always 0.
- The distance between 7/14 and its additive inverse on a number line is: 14
Applications in Algebra
Consider the equation: x + 7/14 = 0
The solution to this equation is x = -7/14, which is the additive inverse of 7/14.
Graphical Representation
On a coordinate plane:
- The point (7/14, 0) is reflected across the y-axis to (-7/14, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 7/14 and Its Additive Inverse
Consider the alternating series: 7/14 + (-7/14) + 7/14 + (-7/14) + ...
The sum of this series oscillates between 0 and 7/14, never converging unless 7/14 is 0.
In Number Theory
For integer values:
- If 7/14 is even, its additive inverse is also even.
- If 7/14 is odd, its additive inverse is also odd.
- The sum of the digits of 7/14 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: