53/67 Additive Inverse :
The additive inverse of 53/67 is -53/67.
This means that when we add 53/67 and -53/67, the result is zero:
53/67 + (-53/67) = 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: 53/67
- Additive inverse: -53/67
To verify: 53/67 + (-53/67) = 0
Extended Mathematical Exploration of 53/67
Let's explore various mathematical operations and concepts related to 53/67 and its additive inverse -53/67.
Basic Operations and Properties
- Square of 53/67: 0.6257518378258
- Cube of 53/67: 0.49499772245921
- Square root of |53/67|: 0.88940698002624
- Reciprocal of 53/67: 1.2641509433962
- Double of 53/67: 1.5820895522388
- Half of 53/67: 0.3955223880597
- Absolute value of 53/67: 0.7910447761194
Trigonometric Functions
- Sine of 53/67: 0.71108824536582
- Cosine of 53/67: 0.70310277150824
- Tangent of 53/67: 1.0113574774289
Exponential and Logarithmic Functions
- e^53/67: 2.2056996852091
- Natural log of 53/67: -0.23440070583884
Floor and Ceiling Functions
- Floor of 53/67: 0
- Ceiling of 53/67: 1
Interesting Properties and Relationships
- The sum of 53/67 and its additive inverse (-53/67) is always 0.
- The product of 53/67 and its additive inverse is: -2809
- The average of 53/67 and its additive inverse is always 0.
- The distance between 53/67 and its additive inverse on a number line is: 106
Applications in Algebra
Consider the equation: x + 53/67 = 0
The solution to this equation is x = -53/67, which is the additive inverse of 53/67.
Graphical Representation
On a coordinate plane:
- The point (53/67, 0) is reflected across the y-axis to (-53/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 53/67 and Its Additive Inverse
Consider the alternating series: 53/67 + (-53/67) + 53/67 + (-53/67) + ...
The sum of this series oscillates between 0 and 53/67, never converging unless 53/67 is 0.
In Number Theory
For integer values:
- If 53/67 is even, its additive inverse is also even.
- If 53/67 is odd, its additive inverse is also odd.
- The sum of the digits of 53/67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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