71/78 Additive Inverse :
The additive inverse of 71/78 is -71/78.
This means that when we add 71/78 and -71/78, the result is zero:
71/78 + (-71/78) = 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: 71/78
- Additive inverse: -71/78
To verify: 71/78 + (-71/78) = 0
Extended Mathematical Exploration of 71/78
Let's explore various mathematical operations and concepts related to 71/78 and its additive inverse -71/78.
Basic Operations and Properties
- Square of 71/78: 0.82856673241289
- Cube of 71/78: 0.75420817950404
- Square root of |71/78|: 0.95407358744303
- Reciprocal of 71/78: 1.0985915492958
- Double of 71/78: 1.8205128205128
- Half of 71/78: 0.45512820512821
- Absolute value of 71/78: 0.91025641025641
Trigonometric Functions
- Sine of 71/78: 0.78966108443978
- Cosine of 71/78: 0.61354329245897
- Tangent of 71/78: 1.2870503094818
Exponential and Logarithmic Functions
- e^71/78: 2.484959620837
- Natural log of 71/78: -0.094028949648276
Floor and Ceiling Functions
- Floor of 71/78: 0
- Ceiling of 71/78: 1
Interesting Properties and Relationships
- The sum of 71/78 and its additive inverse (-71/78) is always 0.
- The product of 71/78 and its additive inverse is: -5041
- The average of 71/78 and its additive inverse is always 0.
- The distance between 71/78 and its additive inverse on a number line is: 142
Applications in Algebra
Consider the equation: x + 71/78 = 0
The solution to this equation is x = -71/78, which is the additive inverse of 71/78.
Graphical Representation
On a coordinate plane:
- The point (71/78, 0) is reflected across the y-axis to (-71/78, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 71/78 and Its Additive Inverse
Consider the alternating series: 71/78 + (-71/78) + 71/78 + (-71/78) + ...
The sum of this series oscillates between 0 and 71/78, never converging unless 71/78 is 0.
In Number Theory
For integer values:
- If 71/78 is even, its additive inverse is also even.
- If 71/78 is odd, its additive inverse is also odd.
- The sum of the digits of 71/78 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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