34/40 Additive Inverse :
The additive inverse of 34/40 is -34/40.
This means that when we add 34/40 and -34/40, the result is zero:
34/40 + (-34/40) = 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: 34/40
- Additive inverse: -34/40
To verify: 34/40 + (-34/40) = 0
Extended Mathematical Exploration of 34/40
Let's explore various mathematical operations and concepts related to 34/40 and its additive inverse -34/40.
Basic Operations and Properties
- Square of 34/40: 0.7225
- Cube of 34/40: 0.614125
- Square root of |34/40|: 0.92195444572929
- Reciprocal of 34/40: 1.1764705882353
- Double of 34/40: 1.7
- Half of 34/40: 0.425
- Absolute value of 34/40: 0.85
Trigonometric Functions
- Sine of 34/40: 0.75128040514029
- Cosine of 34/40: 0.65998314588498
- Tangent of 34/40: 1.1383327132284
Exponential and Logarithmic Functions
- e^34/40: 2.339646851926
- Natural log of 34/40: -0.16251892949777
Floor and Ceiling Functions
- Floor of 34/40: 0
- Ceiling of 34/40: 1
Interesting Properties and Relationships
- The sum of 34/40 and its additive inverse (-34/40) is always 0.
- The product of 34/40 and its additive inverse is: -1156
- The average of 34/40 and its additive inverse is always 0.
- The distance between 34/40 and its additive inverse on a number line is: 68
Applications in Algebra
Consider the equation: x + 34/40 = 0
The solution to this equation is x = -34/40, which is the additive inverse of 34/40.
Graphical Representation
On a coordinate plane:
- The point (34/40, 0) is reflected across the y-axis to (-34/40, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 34/40 and Its Additive Inverse
Consider the alternating series: 34/40 + (-34/40) + 34/40 + (-34/40) + ...
The sum of this series oscillates between 0 and 34/40, never converging unless 34/40 is 0.
In Number Theory
For integer values:
- If 34/40 is even, its additive inverse is also even.
- If 34/40 is odd, its additive inverse is also odd.
- The sum of the digits of 34/40 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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