72/85 Additive Inverse :
The additive inverse of 72/85 is -72/85.
This means that when we add 72/85 and -72/85, the result is zero:
72/85 + (-72/85) = 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: 72/85
- Additive inverse: -72/85
To verify: 72/85 + (-72/85) = 0
Extended Mathematical Exploration of 72/85
Let's explore various mathematical operations and concepts related to 72/85 and its additive inverse -72/85.
Basic Operations and Properties
- Square of 72/85: 0.71750865051903
- Cube of 72/85: 0.60777203338083
- Square root of |72/85|: 0.92035798661684
- Reciprocal of 72/85: 1.1805555555556
- Double of 72/85: 1.6941176470588
- Half of 72/85: 0.42352941176471
- Absolute value of 72/85: 0.84705882352941
Trigonometric Functions
- Sine of 72/85: 0.74933603155888
- Cosine of 72/85: 0.6621899363533
- Tangent of 72/85: 1.1316028686354
Exponential and Logarithmic Functions
- e^72/85: 2.3327756473216
- Natural log of 72/85: -0.16598513747426
Floor and Ceiling Functions
- Floor of 72/85: 0
- Ceiling of 72/85: 1
Interesting Properties and Relationships
- The sum of 72/85 and its additive inverse (-72/85) is always 0.
- The product of 72/85 and its additive inverse is: -5184
- The average of 72/85 and its additive inverse is always 0.
- The distance between 72/85 and its additive inverse on a number line is: 144
Applications in Algebra
Consider the equation: x + 72/85 = 0
The solution to this equation is x = -72/85, which is the additive inverse of 72/85.
Graphical Representation
On a coordinate plane:
- The point (72/85, 0) is reflected across the y-axis to (-72/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 72/85 and Its Additive Inverse
Consider the alternating series: 72/85 + (-72/85) + 72/85 + (-72/85) + ...
The sum of this series oscillates between 0 and 72/85, never converging unless 72/85 is 0.
In Number Theory
For integer values:
- If 72/85 is even, its additive inverse is also even.
- If 72/85 is odd, its additive inverse is also odd.
- The sum of the digits of 72/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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