1/5 Additive Inverse :
The additive inverse of 1/5 is -1/5.
This means that when we add 1/5 and -1/5, the result is zero:
1/5 + (-1/5) = 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: 1/5
- Additive inverse: -1/5
To verify: 1/5 + (-1/5) = 0
Extended Mathematical Exploration of 1/5
Let's explore various mathematical operations and concepts related to 1/5 and its additive inverse -1/5.
Basic Operations and Properties
- Square of 1/5: 0.04
- Cube of 1/5: 0.008
- Square root of |1/5|: 0.44721359549996
- Reciprocal of 1/5: 5
- Double of 1/5: 0.4
- Half of 1/5: 0.1
- Absolute value of 1/5: 0.2
Trigonometric Functions
- Sine of 1/5: 0.19866933079506
- Cosine of 1/5: 0.98006657784124
- Tangent of 1/5: 0.20271003550867
Exponential and Logarithmic Functions
- e^1/5: 1.2214027581602
- Natural log of 1/5: -1.6094379124341
Floor and Ceiling Functions
- Floor of 1/5: 0
- Ceiling of 1/5: 1
Interesting Properties and Relationships
- The sum of 1/5 and its additive inverse (-1/5) is always 0.
- The product of 1/5 and its additive inverse is: -1
- The average of 1/5 and its additive inverse is always 0.
- The distance between 1/5 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/5 = 0
The solution to this equation is x = -1/5, which is the additive inverse of 1/5.
Graphical Representation
On a coordinate plane:
- The point (1/5, 0) is reflected across the y-axis to (-1/5, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/5 and Its Additive Inverse
Consider the alternating series: 1/5 + (-1/5) + 1/5 + (-1/5) + ...
The sum of this series oscillates between 0 and 1/5, never converging unless 1/5 is 0.
In Number Theory
For integer values:
- If 1/5 is even, its additive inverse is also even.
- If 1/5 is odd, its additive inverse is also odd.
- The sum of the digits of 1/5 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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