73/78 Additive Inverse :
The additive inverse of 73/78 is -73/78.
This means that when we add 73/78 and -73/78, the result is zero:
73/78 + (-73/78) = 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: 73/78
- Additive inverse: -73/78
To verify: 73/78 + (-73/78) = 0
Extended Mathematical Exploration of 73/78
Let's explore various mathematical operations and concepts related to 73/78 and its additive inverse -73/78.
Basic Operations and Properties
- Square of 73/78: 0.8759040105194
- Cube of 73/78: 0.81975631753738
- Square root of |73/78|: 0.96741792204685
- Reciprocal of 73/78: 1.0684931506849
- Double of 73/78: 1.8717948717949
- Half of 73/78: 0.46794871794872
- Absolute value of 73/78: 0.93589743589744
Trigonometric Functions
- Sine of 73/78: 0.80513166800434
- Cosine of 73/78: 0.5930961112472
- Tangent of 73/78: 1.3575062333679
Exponential and Logarithmic Functions
- e^73/78: 2.549500444593
- Natural log of 73/78: -0.066249385541201
Floor and Ceiling Functions
- Floor of 73/78: 0
- Ceiling of 73/78: 1
Interesting Properties and Relationships
- The sum of 73/78 and its additive inverse (-73/78) is always 0.
- The product of 73/78 and its additive inverse is: -5329
- The average of 73/78 and its additive inverse is always 0.
- The distance between 73/78 and its additive inverse on a number line is: 146
Applications in Algebra
Consider the equation: x + 73/78 = 0
The solution to this equation is x = -73/78, which is the additive inverse of 73/78.
Graphical Representation
On a coordinate plane:
- The point (73/78, 0) is reflected across the y-axis to (-73/78, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 73/78 and Its Additive Inverse
Consider the alternating series: 73/78 + (-73/78) + 73/78 + (-73/78) + ...
The sum of this series oscillates between 0 and 73/78, never converging unless 73/78 is 0.
In Number Theory
For integer values:
- If 73/78 is even, its additive inverse is also even.
- If 73/78 is odd, its additive inverse is also odd.
- The sum of the digits of 73/78 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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