67/72 Additive Inverse :
The additive inverse of 67/72 is -67/72.
This means that when we add 67/72 and -67/72, the result is zero:
67/72 + (-67/72) = 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: 67/72
- Additive inverse: -67/72
To verify: 67/72 + (-67/72) = 0
Extended Mathematical Exploration of 67/72
Let's explore various mathematical operations and concepts related to 67/72 and its additive inverse -67/72.
Basic Operations and Properties
- Square of 67/72: 0.86593364197531
- Cube of 67/72: 0.80579936128258
- Square root of |67/72|: 0.96465307523252
- Reciprocal of 67/72: 1.0746268656716
- Double of 67/72: 1.8611111111111
- Half of 67/72: 0.46527777777778
- Absolute value of 67/72: 0.93055555555556
Trigonometric Functions
- Sine of 67/72: 0.80195194715007
- Cosine of 67/72: 0.59738854564028
- Tangent of 67/72: 1.3424294004341
Exponential and Logarithmic Functions
- e^67/72: 2.5359176294725
- Natural log of 67/72: -0.071973499625089
Floor and Ceiling Functions
- Floor of 67/72: 0
- Ceiling of 67/72: 1
Interesting Properties and Relationships
- The sum of 67/72 and its additive inverse (-67/72) is always 0.
- The product of 67/72 and its additive inverse is: -4489
- The average of 67/72 and its additive inverse is always 0.
- The distance between 67/72 and its additive inverse on a number line is: 134
Applications in Algebra
Consider the equation: x + 67/72 = 0
The solution to this equation is x = -67/72, which is the additive inverse of 67/72.
Graphical Representation
On a coordinate plane:
- The point (67/72, 0) is reflected across the y-axis to (-67/72, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 67/72 and Its Additive Inverse
Consider the alternating series: 67/72 + (-67/72) + 67/72 + (-67/72) + ...
The sum of this series oscillates between 0 and 67/72, never converging unless 67/72 is 0.
In Number Theory
For integer values:
- If 67/72 is even, its additive inverse is also even.
- If 67/72 is odd, its additive inverse is also odd.
- The sum of the digits of 67/72 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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