75/78 Additive Inverse :
The additive inverse of 75/78 is -75/78.
This means that when we add 75/78 and -75/78, the result is zero:
75/78 + (-75/78) = 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: 75/78
- Additive inverse: -75/78
To verify: 75/78 + (-75/78) = 0
Extended Mathematical Exploration of 75/78
Let's explore various mathematical operations and concepts related to 75/78 and its additive inverse -75/78.
Basic Operations and Properties
- Square of 75/78: 0.92455621301775
- Cube of 75/78: 0.88899635867091
- Square root of |75/78|: 0.98058067569092
- Reciprocal of 75/78: 1.04
- Double of 75/78: 1.9230769230769
- Half of 75/78: 0.48076923076923
- Absolute value of 75/78: 0.96153846153846
Trigonometric Functions
- Sine of 75/78: 0.82007293693576
- Cosine of 75/78: 0.57225901312741
- Tangent of 75/78: 1.4330450340206
Exponential and Logarithmic Functions
- e^75/78: 2.6157175603483
- Natural log of 75/78: -0.039220713153281
Floor and Ceiling Functions
- Floor of 75/78: 0
- Ceiling of 75/78: 1
Interesting Properties and Relationships
- The sum of 75/78 and its additive inverse (-75/78) is always 0.
- The product of 75/78 and its additive inverse is: -5625
- The average of 75/78 and its additive inverse is always 0.
- The distance between 75/78 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/78 = 0
The solution to this equation is x = -75/78, which is the additive inverse of 75/78.
Graphical Representation
On a coordinate plane:
- The point (75/78, 0) is reflected across the y-axis to (-75/78, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/78 and Its Additive Inverse
Consider the alternating series: 75/78 + (-75/78) + 75/78 + (-75/78) + ...
The sum of this series oscillates between 0 and 75/78, never converging unless 75/78 is 0.
In Number Theory
For integer values:
- If 75/78 is even, its additive inverse is also even.
- If 75/78 is odd, its additive inverse is also odd.
- The sum of the digits of 75/78 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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