34/49 Additive Inverse :
The additive inverse of 34/49 is -34/49.
This means that when we add 34/49 and -34/49, the result is zero:
34/49 + (-34/49) = 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: 34/49
- Additive inverse: -34/49
To verify: 34/49 + (-34/49) = 0
Extended Mathematical Exploration of 34/49
Let's explore various mathematical operations and concepts related to 34/49 and its additive inverse -34/49.
Basic Operations and Properties
- Square of 34/49: 0.48146605581008
- Cube of 34/49: 0.33407848770495
- Square root of |34/49|: 0.83299312783504
- Reciprocal of 34/49: 1.4411764705882
- Double of 34/49: 1.3877551020408
- Half of 34/49: 0.3469387755102
- Absolute value of 34/49: 0.69387755102041
Trigonometric Functions
- Sine of 34/49: 0.63952293521021
- Cosine of 34/49: 0.76877201779208
- Tangent of 34/49: 0.83187592733529
Exponential and Logarithmic Functions
- e^34/49: 2.0014612744918
- Natural log of 34/49: -0.36545977349447
Floor and Ceiling Functions
- Floor of 34/49: 0
- Ceiling of 34/49: 1
Interesting Properties and Relationships
- The sum of 34/49 and its additive inverse (-34/49) is always 0.
- The product of 34/49 and its additive inverse is: -1156
- The average of 34/49 and its additive inverse is always 0.
- The distance between 34/49 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34/49 = 0
The solution to this equation is x = -34/49, which is the additive inverse of 34/49.
Graphical Representation
On a coordinate plane:
- The point (34/49, 0) is reflected across the y-axis to (-34/49, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34/49 and Its Additive Inverse
Consider the alternating series: 34/49 + (-34/49) + 34/49 + (-34/49) + ...
The sum of this series oscillates between 0 and 34/49, never converging unless 34/49 is 0.
In Number Theory
For integer values:
- If 34/49 is even, its additive inverse is also even.
- If 34/49 is odd, its additive inverse is also odd.
- The sum of the digits of 34/49 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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