74/85 Additive Inverse :
The additive inverse of 74/85 is -74/85.
This means that when we add 74/85 and -74/85, the result is zero:
74/85 + (-74/85) = 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: 74/85
- Additive inverse: -74/85
To verify: 74/85 + (-74/85) = 0
Extended Mathematical Exploration of 74/85
Let's explore various mathematical operations and concepts related to 74/85 and its additive inverse -74/85.
Basic Operations and Properties
- Square of 74/85: 0.75792387543253
- Cube of 74/85: 0.65983960920008
- Square root of |74/85|: 0.93305317924228
- Reciprocal of 74/85: 1.1486486486486
- Double of 74/85: 1.7411764705882
- Half of 74/85: 0.43529411764706
- Absolute value of 74/85: 0.87058823529412
Trigonometric Functions
- Sine of 74/85: 0.76470811450046
- Cosine of 74/85: 0.64437683044717
- Tangent of 74/85: 1.1867405505095
Exponential and Logarithmic Functions
- e^74/85: 2.3883153317736
- Natural log of 74/85: -0.13858616328615
Floor and Ceiling Functions
- Floor of 74/85: 0
- Ceiling of 74/85: 1
Interesting Properties and Relationships
- The sum of 74/85 and its additive inverse (-74/85) is always 0.
- The product of 74/85 and its additive inverse is: -5476
- The average of 74/85 and its additive inverse is always 0.
- The distance between 74/85 and its additive inverse on a number line is: 148
Applications in Algebra
Consider the equation: x + 74/85 = 0
The solution to this equation is x = -74/85, which is the additive inverse of 74/85.
Graphical Representation
On a coordinate plane:
- The point (74/85, 0) is reflected across the y-axis to (-74/85, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 74/85 and Its Additive Inverse
Consider the alternating series: 74/85 + (-74/85) + 74/85 + (-74/85) + ...
The sum of this series oscillates between 0 and 74/85, never converging unless 74/85 is 0.
In Number Theory
For integer values:
- If 74/85 is even, its additive inverse is also even.
- If 74/85 is odd, its additive inverse is also odd.
- The sum of the digits of 74/85 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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