27/34 Additive Inverse :
The additive inverse of 27/34 is -27/34.
This means that when we add 27/34 and -27/34, the result is zero:
27/34 + (-27/34) = 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: 27/34
- Additive inverse: -27/34
To verify: 27/34 + (-27/34) = 0
Extended Mathematical Exploration of 27/34
Let's explore various mathematical operations and concepts related to 27/34 and its additive inverse -27/34.
Basic Operations and Properties
- Square of 27/34: 0.63062283737024
- Cube of 27/34: 0.50078872379402
- Square root of |27/34|: 0.89113278867901
- Reciprocal of 27/34: 1.2592592592593
- Double of 27/34: 1.5882352941176
- Half of 27/34: 0.39705882352941
- Absolute value of 27/34: 0.79411764705882
Trigonometric Functions
- Sine of 27/34: 0.71324542880417
- Cosine of 27/34: 0.70091437300854
- Tangent of 27/34: 1.0175928134313
Exponential and Logarithmic Functions
- e^27/34: 2.2124879400469
- Natural log of 27/34: -0.23052365861183
Floor and Ceiling Functions
- Floor of 27/34: 0
- Ceiling of 27/34: 1
Interesting Properties and Relationships
- The sum of 27/34 and its additive inverse (-27/34) is always 0.
- The product of 27/34 and its additive inverse is: -729
- The average of 27/34 and its additive inverse is always 0.
- The distance between 27/34 and its additive inverse on a number line is: 54
Applications in Algebra
Consider the equation: x + 27/34 = 0
The solution to this equation is x = -27/34, which is the additive inverse of 27/34.
Graphical Representation
On a coordinate plane:
- The point (27/34, 0) is reflected across the y-axis to (-27/34, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 27/34 and Its Additive Inverse
Consider the alternating series: 27/34 + (-27/34) + 27/34 + (-27/34) + ...
The sum of this series oscillates between 0 and 27/34, never converging unless 27/34 is 0.
In Number Theory
For integer values:
- If 27/34 is even, its additive inverse is also even.
- If 27/34 is odd, its additive inverse is also odd.
- The sum of the digits of 27/34 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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