30/34 Additive Inverse :
The additive inverse of 30/34 is -30/34.
This means that when we add 30/34 and -30/34, the result is zero:
30/34 + (-30/34) = 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: 30/34
- Additive inverse: -30/34
To verify: 30/34 + (-30/34) = 0
Extended Mathematical Exploration of 30/34
Let's explore various mathematical operations and concepts related to 30/34 and its additive inverse -30/34.
Basic Operations and Properties
- Square of 30/34: 0.77854671280277
- Cube of 30/34: 0.6869529818848
- Square root of |30/34|: 0.93933643662772
- Reciprocal of 30/34: 1.1333333333333
- Double of 30/34: 1.7647058823529
- Half of 30/34: 0.44117647058824
- Absolute value of 30/34: 0.88235294117647
Trigonometric Functions
- Sine of 30/34: 0.77223592314622
- Cosine of 30/34: 0.63533587888809
- Tangent of 30/34: 1.2154766459872
Exponential and Logarithmic Functions
- e^30/34: 2.416579090617
- Natural log of 30/34: -0.12516314295401
Floor and Ceiling Functions
- Floor of 30/34: 0
- Ceiling of 30/34: 1
Interesting Properties and Relationships
- The sum of 30/34 and its additive inverse (-30/34) is always 0.
- The product of 30/34 and its additive inverse is: -900
- The average of 30/34 and its additive inverse is always 0.
- The distance between 30/34 and its additive inverse on a number line is: 60
Applications in Algebra
Consider the equation: x + 30/34 = 0
The solution to this equation is x = -30/34, which is the additive inverse of 30/34.
Graphical Representation
On a coordinate plane:
- The point (30/34, 0) is reflected across the y-axis to (-30/34, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 30/34 and Its Additive Inverse
Consider the alternating series: 30/34 + (-30/34) + 30/34 + (-30/34) + ...
The sum of this series oscillates between 0 and 30/34, never converging unless 30/34 is 0.
In Number Theory
For integer values:
- If 30/34 is even, its additive inverse is also even.
- If 30/34 is odd, its additive inverse is also odd.
- The sum of the digits of 30/34 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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