2/5 Additive Inverse :
The additive inverse of 2/5 is -2/5.
This means that when we add 2/5 and -2/5, the result is zero:
2/5 + (-2/5) = 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: 2/5
- Additive inverse: -2/5
To verify: 2/5 + (-2/5) = 0
Extended Mathematical Exploration of 2/5
Let's explore various mathematical operations and concepts related to 2/5 and its additive inverse -2/5.
Basic Operations and Properties
- Square of 2/5: 0.16
- Cube of 2/5: 0.064
- Square root of |2/5|: 0.63245553203368
- Reciprocal of 2/5: 2.5
- Double of 2/5: 0.8
- Half of 2/5: 0.2
- Absolute value of 2/5: 0.4
Trigonometric Functions
- Sine of 2/5: 0.38941834230865
- Cosine of 2/5: 0.92106099400289
- Tangent of 2/5: 0.42279321873816
Exponential and Logarithmic Functions
- e^2/5: 1.4918246976413
- Natural log of 2/5: -0.91629073187415
Floor and Ceiling Functions
- Floor of 2/5: 0
- Ceiling of 2/5: 1
Interesting Properties and Relationships
- The sum of 2/5 and its additive inverse (-2/5) is always 0.
- The product of 2/5 and its additive inverse is: -4
- The average of 2/5 and its additive inverse is always 0.
- The distance between 2/5 and its additive inverse on a number line is: 4
Applications in Algebra
Consider the equation: x + 2/5 = 0
The solution to this equation is x = -2/5, which is the additive inverse of 2/5.
Graphical Representation
On a coordinate plane:
- The point (2/5, 0) is reflected across the y-axis to (-2/5, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 2/5 and Its Additive Inverse
Consider the alternating series: 2/5 + (-2/5) + 2/5 + (-2/5) + ...
The sum of this series oscillates between 0 and 2/5, never converging unless 2/5 is 0.
In Number Theory
For integer values:
- If 2/5 is even, its additive inverse is also even.
- If 2/5 is odd, its additive inverse is also odd.
- The sum of the digits of 2/5 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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