10/14 Additive Inverse :
The additive inverse of 10/14 is -10/14.
This means that when we add 10/14 and -10/14, the result is zero:
10/14 + (-10/14) = 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: 10/14
- Additive inverse: -10/14
To verify: 10/14 + (-10/14) = 0
Extended Mathematical Exploration of 10/14
Let's explore various mathematical operations and concepts related to 10/14 and its additive inverse -10/14.
Basic Operations and Properties
- Square of 10/14: 0.51020408163265
- Cube of 10/14: 0.36443148688047
- Square root of |10/14|: 0.84515425472852
- Reciprocal of 10/14: 1.4
- Double of 10/14: 1.4285714285714
- Half of 10/14: 0.35714285714286
- Absolute value of 10/14: 0.71428571428571
Trigonometric Functions
- Sine of 10/14: 0.65507789717852
- Cosine of 10/14: 0.7555613467007
- Tangent of 10/14: 0.8670082185107
Exponential and Logarithmic Functions
- e^10/14: 2.0427270702661
- Natural log of 10/14: -0.33647223662121
Floor and Ceiling Functions
- Floor of 10/14: 0
- Ceiling of 10/14: 1
Interesting Properties and Relationships
- The sum of 10/14 and its additive inverse (-10/14) is always 0.
- The product of 10/14 and its additive inverse is: -100
- The average of 10/14 and its additive inverse is always 0.
- The distance between 10/14 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/14 = 0
The solution to this equation is x = -10/14, which is the additive inverse of 10/14.
Graphical Representation
On a coordinate plane:
- The point (10/14, 0) is reflected across the y-axis to (-10/14, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/14 and Its Additive Inverse
Consider the alternating series: 10/14 + (-10/14) + 10/14 + (-10/14) + ...
The sum of this series oscillates between 0 and 10/14, never converging unless 10/14 is 0.
In Number Theory
For integer values:
- If 10/14 is even, its additive inverse is also even.
- If 10/14 is odd, its additive inverse is also odd.
- The sum of the digits of 10/14 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: