35/47 Additive Inverse :
The additive inverse of 35/47 is -35/47.
This means that when we add 35/47 and -35/47, the result is zero:
35/47 + (-35/47) = 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: 35/47
- Additive inverse: -35/47
To verify: 35/47 + (-35/47) = 0
Extended Mathematical Exploration of 35/47
Let's explore various mathematical operations and concepts related to 35/47 and its additive inverse -35/47.
Basic Operations and Properties
- Square of 35/47: 0.55454956994115
- Cube of 35/47: 0.41296244570086
- Square root of |35/47|: 0.86294892726269
- Reciprocal of 35/47: 1.3428571428571
- Double of 35/47: 1.4893617021277
- Half of 35/47: 0.37234042553191
- Absolute value of 35/47: 0.74468085106383
Trigonometric Functions
- Sine of 35/47: 0.6777371734099
- Cosine of 35/47: 0.73530423892316
- Tangent of 35/47: 0.92170986856058
Exponential and Logarithmic Functions
- e^35/47: 2.1057692737031
- Natural log of 35/47: -0.29479954022064
Floor and Ceiling Functions
- Floor of 35/47: 0
- Ceiling of 35/47: 1
Interesting Properties and Relationships
- The sum of 35/47 and its additive inverse (-35/47) is always 0.
- The product of 35/47 and its additive inverse is: -1225
- The average of 35/47 and its additive inverse is always 0.
- The distance between 35/47 and its additive inverse on a number line is: 70
Applications in Algebra
Consider the equation: x + 35/47 = 0
The solution to this equation is x = -35/47, which is the additive inverse of 35/47.
Graphical Representation
On a coordinate plane:
- The point (35/47, 0) is reflected across the y-axis to (-35/47, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 35/47 and Its Additive Inverse
Consider the alternating series: 35/47 + (-35/47) + 35/47 + (-35/47) + ...
The sum of this series oscillates between 0 and 35/47, never converging unless 35/47 is 0.
In Number Theory
For integer values:
- If 35/47 is even, its additive inverse is also even.
- If 35/47 is odd, its additive inverse is also odd.
- The sum of the digits of 35/47 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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