27/40 Additive Inverse :
The additive inverse of 27/40 is -27/40.
This means that when we add 27/40 and -27/40, the result is zero:
27/40 + (-27/40) = 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: 27/40
- Additive inverse: -27/40
To verify: 27/40 + (-27/40) = 0
Extended Mathematical Exploration of 27/40
Let's explore various mathematical operations and concepts related to 27/40 and its additive inverse -27/40.
Basic Operations and Properties
- Square of 27/40: 0.455625
- Cube of 27/40: 0.307546875
- Square root of |27/40|: 0.82158383625775
- Reciprocal of 27/40: 1.4814814814815
- Double of 27/40: 1.35
- Half of 27/40: 0.3375
- Absolute value of 27/40: 0.675
Trigonometric Functions
- Sine of 27/40: 0.6248973167277
- Cosine of 27/40: 0.78070695113245
- Tangent of 27/40: 0.80042494283068
Exponential and Logarithmic Functions
- e^27/40: 1.9640329759698
- Natural log of 27/40: -0.39304258810961
Floor and Ceiling Functions
- Floor of 27/40: 0
- Ceiling of 27/40: 1
Interesting Properties and Relationships
- The sum of 27/40 and its additive inverse (-27/40) is always 0.
- The product of 27/40 and its additive inverse is: -729
- The average of 27/40 and its additive inverse is always 0.
- The distance between 27/40 and its additive inverse on a number line is: 54
Applications in Algebra
Consider the equation: x + 27/40 = 0
The solution to this equation is x = -27/40, which is the additive inverse of 27/40.
Graphical Representation
On a coordinate plane:
- The point (27/40, 0) is reflected across the y-axis to (-27/40, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 27/40 and Its Additive Inverse
Consider the alternating series: 27/40 + (-27/40) + 27/40 + (-27/40) + ...
The sum of this series oscillates between 0 and 27/40, never converging unless 27/40 is 0.
In Number Theory
For integer values:
- If 27/40 is even, its additive inverse is also even.
- If 27/40 is odd, its additive inverse is also odd.
- The sum of the digits of 27/40 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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