90/99 Additive Inverse :
The additive inverse of 90/99 is -90/99.
This means that when we add 90/99 and -90/99, the result is zero:
90/99 + (-90/99) = 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: 90/99
- Additive inverse: -90/99
To verify: 90/99 + (-90/99) = 0
Extended Mathematical Exploration of 90/99
Let's explore various mathematical operations and concepts related to 90/99 and its additive inverse -90/99.
Basic Operations and Properties
- Square of 90/99: 0.82644628099174
- Cube of 90/99: 0.75131480090158
- Square root of |90/99|: 0.95346258924559
- Reciprocal of 90/99: 1.1
- Double of 90/99: 1.8181818181818
- Half of 90/99: 0.45454545454545
- Absolute value of 90/99: 0.90909090909091
Trigonometric Functions
- Sine of 90/99: 0.78894546284426
- Cosine of 90/99: 0.61446322644847
- Tangent of 90/99: 1.2839587934404
Exponential and Logarithmic Functions
- e^90/99: 2.482065084623
- Natural log of 90/99: -0.095310179804325
Floor and Ceiling Functions
- Floor of 90/99: 0
- Ceiling of 90/99: 1
Interesting Properties and Relationships
- The sum of 90/99 and its additive inverse (-90/99) is always 0.
- The product of 90/99 and its additive inverse is: -8100
- The average of 90/99 and its additive inverse is always 0.
- The distance between 90/99 and its additive inverse on a number line is: 180
Applications in Algebra
Consider the equation: x + 90/99 = 0
The solution to this equation is x = -90/99, which is the additive inverse of 90/99.
Graphical Representation
On a coordinate plane:
- The point (90/99, 0) is reflected across the y-axis to (-90/99, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 90/99 and Its Additive Inverse
Consider the alternating series: 90/99 + (-90/99) + 90/99 + (-90/99) + ...
The sum of this series oscillates between 0 and 90/99, never converging unless 90/99 is 0.
In Number Theory
For integer values:
- If 90/99 is even, its additive inverse is also even.
- If 90/99 is odd, its additive inverse is also odd.
- The sum of the digits of 90/99 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: