5/8 Additive Inverse :
The additive inverse of 5/8 is -5/8.
This means that when we add 5/8 and -5/8, the result is zero:
5/8 + (-5/8) = 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: 5/8
- Additive inverse: -5/8
To verify: 5/8 + (-5/8) = 0
Extended Mathematical Exploration of 5/8
Let's explore various mathematical operations and concepts related to 5/8 and its additive inverse -5/8.
Basic Operations and Properties
- Square of 5/8: 0.390625
- Cube of 5/8: 0.244140625
- Square root of |5/8|: 0.79056941504209
- Reciprocal of 5/8: 1.6
- Double of 5/8: 1.25
- Half of 5/8: 0.3125
- Absolute value of 5/8: 0.625
Trigonometric Functions
- Sine of 5/8: 0.58509727294046
- Cosine of 5/8: 0.81096311950522
- Tangent of 5/8: 0.7214844409909
Exponential and Logarithmic Functions
- e^5/8: 1.8682459574322
- Natural log of 5/8: -0.47000362924574
Floor and Ceiling Functions
- Floor of 5/8: 0
- Ceiling of 5/8: 1
Interesting Properties and Relationships
- The sum of 5/8 and its additive inverse (-5/8) is always 0.
- The product of 5/8 and its additive inverse is: -25
- The average of 5/8 and its additive inverse is always 0.
- The distance between 5/8 and its additive inverse on a number line is: 10
Applications in Algebra
Consider the equation: x + 5/8 = 0
The solution to this equation is x = -5/8, which is the additive inverse of 5/8.
Graphical Representation
On a coordinate plane:
- The point (5/8, 0) is reflected across the y-axis to (-5/8, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 5/8 and Its Additive Inverse
Consider the alternating series: 5/8 + (-5/8) + 5/8 + (-5/8) + ...
The sum of this series oscillates between 0 and 5/8, never converging unless 5/8 is 0.
In Number Theory
For integer values:
- If 5/8 is even, its additive inverse is also even.
- If 5/8 is odd, its additive inverse is also odd.
- The sum of the digits of 5/8 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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