78/90 Additive Inverse :
The additive inverse of 78/90 is -78/90.
This means that when we add 78/90 and -78/90, the result is zero:
78/90 + (-78/90) = 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: 78/90
- Additive inverse: -78/90
To verify: 78/90 + (-78/90) = 0
Extended Mathematical Exploration of 78/90
Let's explore various mathematical operations and concepts related to 78/90 and its additive inverse -78/90.
Basic Operations and Properties
- Square of 78/90: 0.75111111111111
- Cube of 78/90: 0.65096296296296
- Square root of |78/90|: 0.93094933625126
- Reciprocal of 78/90: 1.1538461538462
- Double of 78/90: 1.7333333333333
- Half of 78/90: 0.43333333333333
- Absolute value of 78/90: 0.86666666666667
Trigonometric Functions
- Sine of 78/90: 0.76217527291384
- Cosine of 78/90: 0.64737072327895
- Tangent of 78/90: 1.1773397305541
Exponential and Logarithmic Functions
- e^78/90: 2.3789677299066
- Natural log of 78/90: -0.14310084364067
Floor and Ceiling Functions
- Floor of 78/90: 0
- Ceiling of 78/90: 1
Interesting Properties and Relationships
- The sum of 78/90 and its additive inverse (-78/90) is always 0.
- The product of 78/90 and its additive inverse is: -6084
- The average of 78/90 and its additive inverse is always 0.
- The distance between 78/90 and its additive inverse on a number line is: 156
Applications in Algebra
Consider the equation: x + 78/90 = 0
The solution to this equation is x = -78/90, which is the additive inverse of 78/90.
Graphical Representation
On a coordinate plane:
- The point (78/90, 0) is reflected across the y-axis to (-78/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 78/90 and Its Additive Inverse
Consider the alternating series: 78/90 + (-78/90) + 78/90 + (-78/90) + ...
The sum of this series oscillates between 0 and 78/90, never converging unless 78/90 is 0.
In Number Theory
For integer values:
- If 78/90 is even, its additive inverse is also even.
- If 78/90 is odd, its additive inverse is also odd.
- The sum of the digits of 78/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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