71/75 Additive Inverse :
The additive inverse of 71/75 is -71/75.
This means that when we add 71/75 and -71/75, the result is zero:
71/75 + (-71/75) = 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: 71/75
- Additive inverse: -71/75
To verify: 71/75 + (-71/75) = 0
Extended Mathematical Exploration of 71/75
Let's explore various mathematical operations and concepts related to 71/75 and its additive inverse -71/75.
Basic Operations and Properties
- Square of 71/75: 0.89617777777778
- Cube of 71/75: 0.84838162962963
- Square root of |71/75|: 0.97296796795509
- Reciprocal of 71/75: 1.056338028169
- Double of 71/75: 1.8933333333333
- Half of 71/75: 0.47333333333333
- Absolute value of 71/75: 0.94666666666667
Trigonometric Functions
- Sine of 71/75: 0.81147204577762
- Cosine of 71/75: 0.58439123788904
- Tangent of 71/75: 1.3885766814521
Exponential and Logarithmic Functions
- e^71/75: 2.5771049762239
- Natural log of 71/75: -0.054808236494995
Floor and Ceiling Functions
- Floor of 71/75: 0
- Ceiling of 71/75: 1
Interesting Properties and Relationships
- The sum of 71/75 and its additive inverse (-71/75) is always 0.
- The product of 71/75 and its additive inverse is: -5041
- The average of 71/75 and its additive inverse is always 0.
- The distance between 71/75 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/75 = 0
The solution to this equation is x = -71/75, which is the additive inverse of 71/75.
Graphical Representation
On a coordinate plane:
- The point (71/75, 0) is reflected across the y-axis to (-71/75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/75 and Its Additive Inverse
Consider the alternating series: 71/75 + (-71/75) + 71/75 + (-71/75) + ...
The sum of this series oscillates between 0 and 71/75, never converging unless 71/75 is 0.
In Number Theory
For integer values:
- If 71/75 is even, its additive inverse is also even.
- If 71/75 is odd, its additive inverse is also odd.
- The sum of the digits of 71/75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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