4/5 Additive Inverse :
The additive inverse of 4/5 is -4/5.
This means that when we add 4/5 and -4/5, the result is zero:
4/5 + (-4/5) = 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: 4/5
- Additive inverse: -4/5
To verify: 4/5 + (-4/5) = 0
Extended Mathematical Exploration of 4/5
Let's explore various mathematical operations and concepts related to 4/5 and its additive inverse -4/5.
Basic Operations and Properties
- Square of 4/5: 0.64
- Cube of 4/5: 0.512
- Square root of |4/5|: 0.89442719099992
- Reciprocal of 4/5: 1.25
- Double of 4/5: 1.6
- Half of 4/5: 0.4
- Absolute value of 4/5: 0.8
Trigonometric Functions
- Sine of 4/5: 0.71735609089952
- Cosine of 4/5: 0.69670670934717
- Tangent of 4/5: 1.0296385570504
Exponential and Logarithmic Functions
- e^4/5: 2.2255409284925
- Natural log of 4/5: -0.22314355131421
Floor and Ceiling Functions
- Floor of 4/5: 0
- Ceiling of 4/5: 1
Interesting Properties and Relationships
- The sum of 4/5 and its additive inverse (-4/5) is always 0.
- The product of 4/5 and its additive inverse is: -16
- The average of 4/5 and its additive inverse is always 0.
- The distance between 4/5 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4/5 = 0
The solution to this equation is x = -4/5, which is the additive inverse of 4/5.
Graphical Representation
On a coordinate plane:
- The point (4/5, 0) is reflected across the y-axis to (-4/5, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4/5 and Its Additive Inverse
Consider the alternating series: 4/5 + (-4/5) + 4/5 + (-4/5) + ...
The sum of this series oscillates between 0 and 4/5, never converging unless 4/5 is 0.
In Number Theory
For integer values:
- If 4/5 is even, its additive inverse is also even.
- If 4/5 is odd, its additive inverse is also odd.
- The sum of the digits of 4/5 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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