5/7 Additive Inverse :
The additive inverse of 5/7 is -5/7.
This means that when we add 5/7 and -5/7, the result is zero:
5/7 + (-5/7) = 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: 5/7
- Additive inverse: -5/7
To verify: 5/7 + (-5/7) = 0
Extended Mathematical Exploration of 5/7
Let's explore various mathematical operations and concepts related to 5/7 and its additive inverse -5/7.
Basic Operations and Properties
- Square of 5/7: 0.51020408163265
- Cube of 5/7: 0.36443148688047
- Square root of |5/7|: 0.84515425472852
- Reciprocal of 5/7: 1.4
- Double of 5/7: 1.4285714285714
- Half of 5/7: 0.35714285714286
- Absolute value of 5/7: 0.71428571428571
Trigonometric Functions
- Sine of 5/7: 0.65507789717852
- Cosine of 5/7: 0.7555613467007
- Tangent of 5/7: 0.8670082185107
Exponential and Logarithmic Functions
- e^5/7: 2.0427270702661
- Natural log of 5/7: -0.33647223662121
Floor and Ceiling Functions
- Floor of 5/7: 0
- Ceiling of 5/7: 1
Interesting Properties and Relationships
- The sum of 5/7 and its additive inverse (-5/7) is always 0.
- The product of 5/7 and its additive inverse is: -25
- The average of 5/7 and its additive inverse is always 0.
- The distance between 5/7 and its additive inverse on a number line is: 10
Applications in Algebra
Consider the equation: x + 5/7 = 0
The solution to this equation is x = -5/7, which is the additive inverse of 5/7.
Graphical Representation
On a coordinate plane:
- The point (5/7, 0) is reflected across the y-axis to (-5/7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 5/7 and Its Additive Inverse
Consider the alternating series: 5/7 + (-5/7) + 5/7 + (-5/7) + ...
The sum of this series oscillates between 0 and 5/7, never converging unless 5/7 is 0.
In Number Theory
For integer values:
- If 5/7 is even, its additive inverse is also even.
- If 5/7 is odd, its additive inverse is also odd.
- The sum of the digits of 5/7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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