42/45 Additive Inverse :
The additive inverse of 42/45 is -42/45.
This means that when we add 42/45 and -42/45, the result is zero:
42/45 + (-42/45) = 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: 42/45
- Additive inverse: -42/45
To verify: 42/45 + (-42/45) = 0
Extended Mathematical Exploration of 42/45
Let's explore various mathematical operations and concepts related to 42/45 and its additive inverse -42/45.
Basic Operations and Properties
- Square of 42/45: 0.87111111111111
- Cube of 42/45: 0.81303703703704
- Square root of |42/45|: 0.9660917830793
- Reciprocal of 42/45: 1.0714285714286
- Double of 42/45: 1.8666666666667
- Half of 42/45: 0.46666666666667
- Absolute value of 42/45: 0.93333333333333
Trigonometric Functions
- Sine of 42/45: 0.80360826369441
- Cosine of 42/45: 0.59515859946913
- Tangent of 42/45: 1.3502422117587
Exponential and Logarithmic Functions
- e^42/45: 2.542971637808
- Natural log of 42/45: -0.068992871486951
Floor and Ceiling Functions
- Floor of 42/45: 0
- Ceiling of 42/45: 1
Interesting Properties and Relationships
- The sum of 42/45 and its additive inverse (-42/45) is always 0.
- The product of 42/45 and its additive inverse is: -1764
- The average of 42/45 and its additive inverse is always 0.
- The distance between 42/45 and its additive inverse on a number line is: 84
Applications in Algebra
Consider the equation: x + 42/45 = 0
The solution to this equation is x = -42/45, which is the additive inverse of 42/45.
Graphical Representation
On a coordinate plane:
- The point (42/45, 0) is reflected across the y-axis to (-42/45, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 42/45 and Its Additive Inverse
Consider the alternating series: 42/45 + (-42/45) + 42/45 + (-42/45) + ...
The sum of this series oscillates between 0 and 42/45, never converging unless 42/45 is 0.
In Number Theory
For integer values:
- If 42/45 is even, its additive inverse is also even.
- If 42/45 is odd, its additive inverse is also odd.
- The sum of the digits of 42/45 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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