11/16 Additive Inverse :
The additive inverse of 11/16 is -11/16.
This means that when we add 11/16 and -11/16, the result is zero:
11/16 + (-11/16) = 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: 11/16
- Additive inverse: -11/16
To verify: 11/16 + (-11/16) = 0
Extended Mathematical Exploration of 11/16
Let's explore various mathematical operations and concepts related to 11/16 and its additive inverse -11/16.
Basic Operations and Properties
- Square of 11/16: 0.47265625
- Cube of 11/16: 0.324951171875
- Square root of |11/16|: 0.82915619758885
- Reciprocal of 11/16: 1.4545454545455
- Double of 11/16: 1.375
- Half of 11/16: 0.34375
- Absolute value of 11/16: 0.6875
Trigonometric Functions
- Sine of 11/16: 0.63460708001527
- Cosine of 11/16: 0.77283494615247
- Tangent of 11/16: 0.82114180158989
Exponential and Logarithmic Functions
- e^11/16: 1.9887374695823
- Natural log of 11/16: -0.37469344944141
Floor and Ceiling Functions
- Floor of 11/16: 0
- Ceiling of 11/16: 1
Interesting Properties and Relationships
- The sum of 11/16 and its additive inverse (-11/16) is always 0.
- The product of 11/16 and its additive inverse is: -121
- The average of 11/16 and its additive inverse is always 0.
- The distance between 11/16 and its additive inverse on a number line is: 22
Applications in Algebra
Consider the equation: x + 11/16 = 0
The solution to this equation is x = -11/16, which is the additive inverse of 11/16.
Graphical Representation
On a coordinate plane:
- The point (11/16, 0) is reflected across the y-axis to (-11/16, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 11/16 and Its Additive Inverse
Consider the alternating series: 11/16 + (-11/16) + 11/16 + (-11/16) + ...
The sum of this series oscillates between 0 and 11/16, never converging unless 11/16 is 0.
In Number Theory
For integer values:
- If 11/16 is even, its additive inverse is also even.
- If 11/16 is odd, its additive inverse is also odd.
- The sum of the digits of 11/16 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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