3/7 Additive Inverse :
The additive inverse of 3/7 is -3/7.
This means that when we add 3/7 and -3/7, the result is zero:
3/7 + (-3/7) = 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: 3/7
- Additive inverse: -3/7
To verify: 3/7 + (-3/7) = 0
Extended Mathematical Exploration of 3/7
Let's explore various mathematical operations and concepts related to 3/7 and its additive inverse -3/7.
Basic Operations and Properties
- Square of 3/7: 0.18367346938776
- Cube of 3/7: 0.078717201166181
- Square root of |3/7|: 0.65465367070798
- Reciprocal of 3/7: 2.3333333333333
- Double of 3/7: 0.85714285714286
- Half of 3/7: 0.21428571428571
- Absolute value of 3/7: 0.42857142857143
Trigonometric Functions
- Sine of 3/7: 0.41557185499305
- Cosine of 3/7: 0.90956035167417
- Tangent of 3/7: 0.45689310690394
Exponential and Logarithmic Functions
- e^3/7: 1.5350630092552
- Natural log of 3/7: -0.8472978603872
Floor and Ceiling Functions
- Floor of 3/7: 0
- Ceiling of 3/7: 1
Interesting Properties and Relationships
- The sum of 3/7 and its additive inverse (-3/7) is always 0.
- The product of 3/7 and its additive inverse is: -9
- The average of 3/7 and its additive inverse is always 0.
- The distance between 3/7 and its additive inverse on a number line is: 6
Applications in Algebra
Consider the equation: x + 3/7 = 0
The solution to this equation is x = -3/7, which is the additive inverse of 3/7.
Graphical Representation
On a coordinate plane:
- The point (3/7, 0) is reflected across the y-axis to (-3/7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 3/7 and Its Additive Inverse
Consider the alternating series: 3/7 + (-3/7) + 3/7 + (-3/7) + ...
The sum of this series oscillates between 0 and 3/7, never converging unless 3/7 is 0.
In Number Theory
For integer values:
- If 3/7 is even, its additive inverse is also even.
- If 3/7 is odd, its additive inverse is also odd.
- The sum of the digits of 3/7 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: