34/45 Additive Inverse :
The additive inverse of 34/45 is -34/45.
This means that when we add 34/45 and -34/45, the result is zero:
34/45 + (-34/45) = 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: 34/45
- Additive inverse: -34/45
To verify: 34/45 + (-34/45) = 0
Extended Mathematical Exploration of 34/45
Let's explore various mathematical operations and concepts related to 34/45 and its additive inverse -34/45.
Basic Operations and Properties
- Square of 34/45: 0.57086419753086
- Cube of 34/45: 0.43131961591221
- Square root of |34/45|: 0.86922698736035
- Reciprocal of 34/45: 1.3235294117647
- Double of 34/45: 1.5111111111111
- Half of 34/45: 0.37777777777778
- Absolute value of 34/45: 0.75555555555556
Trigonometric Functions
- Sine of 34/45: 0.68569315818399
- Cosine of 34/45: 0.72789071488766
- Tangent of 34/45: 0.94202762057463
Exponential and Logarithmic Functions
- e^34/45: 2.1287938581531
- Natural log of 34/45: -0.28030196515416
Floor and Ceiling Functions
- Floor of 34/45: 0
- Ceiling of 34/45: 1
Interesting Properties and Relationships
- The sum of 34/45 and its additive inverse (-34/45) is always 0.
- The product of 34/45 and its additive inverse is: -1156
- The average of 34/45 and its additive inverse is always 0.
- The distance between 34/45 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34/45 = 0
The solution to this equation is x = -34/45, which is the additive inverse of 34/45.
Graphical Representation
On a coordinate plane:
- The point (34/45, 0) is reflected across the y-axis to (-34/45, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34/45 and Its Additive Inverse
Consider the alternating series: 34/45 + (-34/45) + 34/45 + (-34/45) + ...
The sum of this series oscillates between 0 and 34/45, never converging unless 34/45 is 0.
In Number Theory
For integer values:
- If 34/45 is even, its additive inverse is also even.
- If 34/45 is odd, its additive inverse is also odd.
- The sum of the digits of 34/45 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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