61/67 Additive Inverse :
The additive inverse of 61/67 is -61/67.
This means that when we add 61/67 and -61/67, the result is zero:
61/67 + (-61/67) = 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: 61/67
- Additive inverse: -61/67
To verify: 61/67 + (-61/67) = 0
Extended Mathematical Exploration of 61/67
Let's explore various mathematical operations and concepts related to 61/67 and its additive inverse -61/67.
Basic Operations and Properties
- Square of 61/67: 0.82891512586322
- Cube of 61/67: 0.75468392056204
- Square root of |61/67|: 0.95417386318953
- Reciprocal of 61/67: 1.0983606557377
- Double of 61/67: 1.8208955223881
- Half of 61/67: 0.45522388059701
- Absolute value of 61/67: 0.91044776119403
Trigonometric Functions
- Sine of 61/67: 0.78977847206655
- Cosine of 61/67: 0.61339217883848
- Tangent of 61/67: 1.2875587581864
Exponential and Logarithmic Functions
- e^61/67: 2.4854351656869
- Natural log of 61/67: -0.093818755217655
Floor and Ceiling Functions
- Floor of 61/67: 0
- Ceiling of 61/67: 1
Interesting Properties and Relationships
- The sum of 61/67 and its additive inverse (-61/67) is always 0.
- The product of 61/67 and its additive inverse is: -3721
- The average of 61/67 and its additive inverse is always 0.
- The distance between 61/67 and its additive inverse on a number line is: 122
Applications in Algebra
Consider the equation: x + 61/67 = 0
The solution to this equation is x = -61/67, which is the additive inverse of 61/67.
Graphical Representation
On a coordinate plane:
- The point (61/67, 0) is reflected across the y-axis to (-61/67, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 61/67 and Its Additive Inverse
Consider the alternating series: 61/67 + (-61/67) + 61/67 + (-61/67) + ...
The sum of this series oscillates between 0 and 61/67, never converging unless 61/67 is 0.
In Number Theory
For integer values:
- If 61/67 is even, its additive inverse is also even.
- If 61/67 is odd, its additive inverse is also odd.
- The sum of the digits of 61/67 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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