60/67 Additive Inverse :
The additive inverse of 60/67 is -60/67.
This means that when we add 60/67 and -60/67, the result is zero:
60/67 + (-60/67) = 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: 60/67
- Additive inverse: -60/67
To verify: 60/67 + (-60/67) = 0
Extended Mathematical Exploration of 60/67
Let's explore various mathematical operations and concepts related to 60/67 and its additive inverse -60/67.
Basic Operations and Properties
- Square of 60/67: 0.80196034751615
- Cube of 60/67: 0.71817344553685
- Square root of |60/67|: 0.94632044681477
- Reciprocal of 60/67: 1.1166666666667
- Double of 60/67: 1.7910447761194
- Half of 60/67: 0.44776119402985
- Absolute value of 60/67: 0.8955223880597
Trigonometric Functions
- Sine of 60/67: 0.78053573826094
- Cosine of 60/67: 0.62511115915287
- Tangent of 60/67: 1.2486351056646
Exponential and Logarithmic Functions
- e^60/67: 2.4486145824408
- Natural log of 60/67: -0.11034805716887
Floor and Ceiling Functions
- Floor of 60/67: 0
- Ceiling of 60/67: 1
Interesting Properties and Relationships
- The sum of 60/67 and its additive inverse (-60/67) is always 0.
- The product of 60/67 and its additive inverse is: -3600
- The average of 60/67 and its additive inverse is always 0.
- The distance between 60/67 and its additive inverse on a number line is: 120
Applications in Algebra
Consider the equation: x + 60/67 = 0
The solution to this equation is x = -60/67, which is the additive inverse of 60/67.
Graphical Representation
On a coordinate plane:
- The point (60/67, 0) is reflected across the y-axis to (-60/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 60/67 and Its Additive Inverse
Consider the alternating series: 60/67 + (-60/67) + 60/67 + (-60/67) + ...
The sum of this series oscillates between 0 and 60/67, never converging unless 60/67 is 0.
In Number Theory
For integer values:
- If 60/67 is even, its additive inverse is also even.
- If 60/67 is odd, its additive inverse is also odd.
- The sum of the digits of 60/67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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