4/7 Additive Inverse :
The additive inverse of 4/7 is -4/7.
This means that when we add 4/7 and -4/7, the result is zero:
4/7 + (-4/7) = 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: 4/7
- Additive inverse: -4/7
To verify: 4/7 + (-4/7) = 0
Extended Mathematical Exploration of 4/7
Let's explore various mathematical operations and concepts related to 4/7 and its additive inverse -4/7.
Basic Operations and Properties
- Square of 4/7: 0.3265306122449
- Cube of 4/7: 0.1865889212828
- Square root of |4/7|: 0.75592894601845
- Reciprocal of 4/7: 1.75
- Double of 4/7: 1.1428571428571
- Half of 4/7: 0.28571428571429
- Absolute value of 4/7: 0.57142857142857
Trigonometric Functions
- Sine of 4/7: 0.54083421335883
- Cosine of 4/7: 0.84112921341524
- Tangent of 4/7: 0.64298588698743
Exponential and Logarithmic Functions
- e^4/7: 1.7707949524352
- Natural log of 4/7: -0.55961578793542
Floor and Ceiling Functions
- Floor of 4/7: 0
- Ceiling of 4/7: 1
Interesting Properties and Relationships
- The sum of 4/7 and its additive inverse (-4/7) is always 0.
- The product of 4/7 and its additive inverse is: -16
- The average of 4/7 and its additive inverse is always 0.
- The distance between 4/7 and its additive inverse on a number line is: 8
Applications in Algebra
Consider the equation: x + 4/7 = 0
The solution to this equation is x = -4/7, which is the additive inverse of 4/7.
Graphical Representation
On a coordinate plane:
- The point (4/7, 0) is reflected across the y-axis to (-4/7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 4/7 and Its Additive Inverse
Consider the alternating series: 4/7 + (-4/7) + 4/7 + (-4/7) + ...
The sum of this series oscillates between 0 and 4/7, never converging unless 4/7 is 0.
In Number Theory
For integer values:
- If 4/7 is even, its additive inverse is also even.
- If 4/7 is odd, its additive inverse is also odd.
- The sum of the digits of 4/7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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