16 Additive Inverse :
The additive inverse of 16 is -16.
This means that when we add 16 and -16, the result is zero:
16 + (-16) = 0
Additive Inverse of a Whole Number
For whole numbers, the additive inverse is the negative of that number:
- Original number: 16
- Additive inverse: -16
To verify: 16 + (-16) = 0
Extended Mathematical Exploration of 16
Let's explore various mathematical operations and concepts related to 16 and its additive inverse -16.
Basic Operations and Properties
- Square of 16: 256
- Cube of 16: 4096
- Square root of |16|: 4
- Reciprocal of 16: 0.0625
- Double of 16: 32
- Half of 16: 8
- Absolute value of 16: 16
Trigonometric Functions
- Sine of 16: -0.28790331666507
- Cosine of 16: -0.95765948032338
- Tangent of 16: 0.3006322420239
Exponential and Logarithmic Functions
- e^16: 8886110.5205079
- Natural log of 16: 2.7725887222398
Floor and Ceiling Functions
- Floor of 16: 16
- Ceiling of 16: 16
Interesting Properties and Relationships
- The sum of 16 and its additive inverse (-16) is always 0.
- The product of 16 and its additive inverse is: -256
- The average of 16 and its additive inverse is always 0.
- The distance between 16 and its additive inverse on a number line is: 32
Applications in Algebra
Consider the equation: x + 16 = 0
The solution to this equation is x = -16, which is the additive inverse of 16.
Graphical Representation
On a coordinate plane:
- The point (16, 0) is reflected across the y-axis to (-16, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 16 and Its Additive Inverse
Consider the alternating series: 16 + (-16) + 16 + (-16) + ...
The sum of this series oscillates between 0 and 16, never converging unless 16 is 0.
In Number Theory
For integer values:
- If 16 is even, its additive inverse is also even.
- If 16 is odd, its additive inverse is also odd.
- The sum of the digits of 16 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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