37/45 Additive Inverse :
The additive inverse of 37/45 is -37/45.
This means that when we add 37/45 and -37/45, the result is zero:
37/45 + (-37/45) = 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: 37/45
- Additive inverse: -37/45
To verify: 37/45 + (-37/45) = 0
Extended Mathematical Exploration of 37/45
Let's explore various mathematical operations and concepts related to 37/45 and its additive inverse -37/45.
Basic Operations and Properties
- Square of 37/45: 0.67604938271605
- Cube of 37/45: 0.55586282578875
- Square root of |37/45|: 0.90676470058236
- Reciprocal of 37/45: 1.2162162162162
- Double of 37/45: 1.6444444444444
- Half of 37/45: 0.41111111111111
- Absolute value of 37/45: 0.82222222222222
Trigonometric Functions
- Sine of 37/45: 0.73266007030882
- Cosine of 37/45: 0.68059475561825
- Tangent of 37/45: 1.0764997294804
Exponential and Logarithmic Functions
- e^37/45: 2.2755510030544
- Natural log of 37/45: -0.1957445771261
Floor and Ceiling Functions
- Floor of 37/45: 0
- Ceiling of 37/45: 1
Interesting Properties and Relationships
- The sum of 37/45 and its additive inverse (-37/45) is always 0.
- The product of 37/45 and its additive inverse is: -1369
- The average of 37/45 and its additive inverse is always 0.
- The distance between 37/45 and its additive inverse on a number line is: 74
Applications in Algebra
Consider the equation: x + 37/45 = 0
The solution to this equation is x = -37/45, which is the additive inverse of 37/45.
Graphical Representation
On a coordinate plane:
- The point (37/45, 0) is reflected across the y-axis to (-37/45, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 37/45 and Its Additive Inverse
Consider the alternating series: 37/45 + (-37/45) + 37/45 + (-37/45) + ...
The sum of this series oscillates between 0 and 37/45, never converging unless 37/45 is 0.
In Number Theory
For integer values:
- If 37/45 is even, its additive inverse is also even.
- If 37/45 is odd, its additive inverse is also odd.
- The sum of the digits of 37/45 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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