34/42 Additive Inverse :
The additive inverse of 34/42 is -34/42.
This means that when we add 34/42 and -34/42, the result is zero:
34/42 + (-34/42) = 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: 34/42
- Additive inverse: -34/42
To verify: 34/42 + (-34/42) = 0
Extended Mathematical Exploration of 34/42
Let's explore various mathematical operations and concepts related to 34/42 and its additive inverse -34/42.
Basic Operations and Properties
- Square of 34/42: 0.65532879818594
- Cube of 34/42: 0.53050426519814
- Square root of |34/42|: 0.89973541084244
- Reciprocal of 34/42: 1.2352941176471
- Double of 34/42: 1.6190476190476
- Half of 34/42: 0.4047619047619
- Absolute value of 34/42: 0.80952380952381
Trigonometric Functions
- Sine of 34/42: 0.72395875967671
- Cosine of 34/42: 0.68984325341875
- Tangent of 34/42: 1.0494539971057
Exponential and Logarithmic Functions
- e^34/42: 2.2468378091263
- Natural log of 34/42: -0.21130909366721
Floor and Ceiling Functions
- Floor of 34/42: 0
- Ceiling of 34/42: 1
Interesting Properties and Relationships
- The sum of 34/42 and its additive inverse (-34/42) is always 0.
- The product of 34/42 and its additive inverse is: -1156
- The average of 34/42 and its additive inverse is always 0.
- The distance between 34/42 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34/42 = 0
The solution to this equation is x = -34/42, which is the additive inverse of 34/42.
Graphical Representation
On a coordinate plane:
- The point (34/42, 0) is reflected across the y-axis to (-34/42, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34/42 and Its Additive Inverse
Consider the alternating series: 34/42 + (-34/42) + 34/42 + (-34/42) + ...
The sum of this series oscillates between 0 and 34/42, never converging unless 34/42 is 0.
In Number Theory
For integer values:
- If 34/42 is even, its additive inverse is also even.
- If 34/42 is odd, its additive inverse is also odd.
- The sum of the digits of 34/42 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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