4/10 Additive Inverse :
The additive inverse of 4/10 is -4/10.
This means that when we add 4/10 and -4/10, the result is zero:
4/10 + (-4/10) = 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: 4/10
- Additive inverse: -4/10
To verify: 4/10 + (-4/10) = 0
Extended Mathematical Exploration of 4/10
Let's explore various mathematical operations and concepts related to 4/10 and its additive inverse -4/10.
Basic Operations and Properties
- Square of 4/10: 0.16
- Cube of 4/10: 0.064
- Square root of |4/10|: 0.63245553203368
- Reciprocal of 4/10: 2.5
- Double of 4/10: 0.8
- Half of 4/10: 0.2
- Absolute value of 4/10: 0.4
Trigonometric Functions
- Sine of 4/10: 0.38941834230865
- Cosine of 4/10: 0.92106099400289
- Tangent of 4/10: 0.42279321873816
Exponential and Logarithmic Functions
- e^4/10: 1.4918246976413
- Natural log of 4/10: -0.91629073187415
Floor and Ceiling Functions
- Floor of 4/10: 0
- Ceiling of 4/10: 1
Interesting Properties and Relationships
- The sum of 4/10 and its additive inverse (-4/10) is always 0.
- The product of 4/10 and its additive inverse is: -16
- The average of 4/10 and its additive inverse is always 0.
- The distance between 4/10 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4/10 = 0
The solution to this equation is x = -4/10, which is the additive inverse of 4/10.
Graphical Representation
On a coordinate plane:
- The point (4/10, 0) is reflected across the y-axis to (-4/10, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4/10 and Its Additive Inverse
Consider the alternating series: 4/10 + (-4/10) + 4/10 + (-4/10) + ...
The sum of this series oscillates between 0 and 4/10, never converging unless 4/10 is 0.
In Number Theory
For integer values:
- If 4/10 is even, its additive inverse is also even.
- If 4/10 is odd, its additive inverse is also odd.
- The sum of the digits of 4/10 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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