27/35 Additive Inverse :
The additive inverse of 27/35 is -27/35.
This means that when we add 27/35 and -27/35, the result is zero:
27/35 + (-27/35) = 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: 27/35
- Additive inverse: -27/35
To verify: 27/35 + (-27/35) = 0
Extended Mathematical Exploration of 27/35
Let's explore various mathematical operations and concepts related to 27/35 and its additive inverse -27/35.
Basic Operations and Properties
- Square of 27/35: 0.59510204081633
- Cube of 27/35: 0.45907871720117
- Square root of |27/35|: 0.87831006565368
- Reciprocal of 27/35: 1.2962962962963
- Double of 27/35: 1.5428571428571
- Half of 27/35: 0.38571428571429
- Absolute value of 27/35: 0.77142857142857
Trigonometric Functions
- Sine of 27/35: 0.69716011460743
- Cosine of 27/35: 0.71691545847509
- Tangent of 27/35: 0.97244397001889
Exponential and Logarithmic Functions
- e^27/35: 2.1628538390404
- Natural log of 27/35: -0.25951119548508
Floor and Ceiling Functions
- Floor of 27/35: 0
- Ceiling of 27/35: 1
Interesting Properties and Relationships
- The sum of 27/35 and its additive inverse (-27/35) is always 0.
- The product of 27/35 and its additive inverse is: -729
- The average of 27/35 and its additive inverse is always 0.
- The distance between 27/35 and its additive inverse on a number line is: 54
Applications in Algebra
Consider the equation: x + 27/35 = 0
The solution to this equation is x = -27/35, which is the additive inverse of 27/35.
Graphical Representation
On a coordinate plane:
- The point (27/35, 0) is reflected across the y-axis to (-27/35, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 27/35 and Its Additive Inverse
Consider the alternating series: 27/35 + (-27/35) + 27/35 + (-27/35) + ...
The sum of this series oscillates between 0 and 27/35, never converging unless 27/35 is 0.
In Number Theory
For integer values:
- If 27/35 is even, its additive inverse is also even.
- If 27/35 is odd, its additive inverse is also odd.
- The sum of the digits of 27/35 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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