75/90 Additive Inverse :
The additive inverse of 75/90 is -75/90.
This means that when we add 75/90 and -75/90, the result is zero:
75/90 + (-75/90) = 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: 75/90
- Additive inverse: -75/90
To verify: 75/90 + (-75/90) = 0
Extended Mathematical Exploration of 75/90
Let's explore various mathematical operations and concepts related to 75/90 and its additive inverse -75/90.
Basic Operations and Properties
- Square of 75/90: 0.69444444444444
- Cube of 75/90: 0.5787037037037
- Square root of |75/90|: 0.91287092917528
- Reciprocal of 75/90: 1.2
- Double of 75/90: 1.6666666666667
- Half of 75/90: 0.41666666666667
- Absolute value of 75/90: 0.83333333333333
Trigonometric Functions
- Sine of 75/90: 0.74017685319604
- Cosine of 75/90: 0.67241224408306
- Tangent of 75/90: 1.1007783687898
Exponential and Logarithmic Functions
- e^75/90: 2.3009758908928
- Natural log of 75/90: -0.18232155679395
Floor and Ceiling Functions
- Floor of 75/90: 0
- Ceiling of 75/90: 1
Interesting Properties and Relationships
- The sum of 75/90 and its additive inverse (-75/90) is always 0.
- The product of 75/90 and its additive inverse is: -5625
- The average of 75/90 and its additive inverse is always 0.
- The distance between 75/90 and its additive inverse on a number line is: 150
Applications in Algebra
Consider the equation: x + 75/90 = 0
The solution to this equation is x = -75/90, which is the additive inverse of 75/90.
Graphical Representation
On a coordinate plane:
- The point (75/90, 0) is reflected across the y-axis to (-75/90, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 75/90 and Its Additive Inverse
Consider the alternating series: 75/90 + (-75/90) + 75/90 + (-75/90) + ...
The sum of this series oscillates between 0 and 75/90, never converging unless 75/90 is 0.
In Number Theory
For integer values:
- If 75/90 is even, its additive inverse is also even.
- If 75/90 is odd, its additive inverse is also odd.
- The sum of the digits of 75/90 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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