34/43 Additive Inverse :
The additive inverse of 34/43 is -34/43.
This means that when we add 34/43 and -34/43, the result is zero:
34/43 + (-34/43) = 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: 34/43
- Additive inverse: -34/43
To verify: 34/43 + (-34/43) = 0
Extended Mathematical Exploration of 34/43
Let's explore various mathematical operations and concepts related to 34/43 and its additive inverse -34/43.
Basic Operations and Properties
- Square of 34/43: 0.62520281233099
- Cube of 34/43: 0.49434640975008
- Square root of |34/43|: 0.8892118276421
- Reciprocal of 34/43: 1.2647058823529
- Double of 34/43: 1.5813953488372
- Half of 34/43: 0.3953488372093
- Absolute value of 34/43: 0.7906976744186
Trigonometric Functions
- Sine of 34/43: 0.71084415436708
- Cosine of 34/43: 0.7033495490879
- Tangent of 34/43: 1.010655591219
Exponential and Logarithmic Functions
- e^34/43: 2.2049342159525
- Natural log of 34/43: -0.2348395910774
Floor and Ceiling Functions
- Floor of 34/43: 0
- Ceiling of 34/43: 1
Interesting Properties and Relationships
- The sum of 34/43 and its additive inverse (-34/43) is always 0.
- The product of 34/43 and its additive inverse is: -1156
- The average of 34/43 and its additive inverse is always 0.
- The distance between 34/43 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34/43 = 0
The solution to this equation is x = -34/43, which is the additive inverse of 34/43.
Graphical Representation
On a coordinate plane:
- The point (34/43, 0) is reflected across the y-axis to (-34/43, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34/43 and Its Additive Inverse
Consider the alternating series: 34/43 + (-34/43) + 34/43 + (-34/43) + ...
The sum of this series oscillates between 0 and 34/43, never converging unless 34/43 is 0.
In Number Theory
For integer values:
- If 34/43 is even, its additive inverse is also even.
- If 34/43 is odd, its additive inverse is also odd.
- The sum of the digits of 34/43 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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