42/49 Additive Inverse :
The additive inverse of 42/49 is -42/49.
This means that when we add 42/49 and -42/49, the result is zero:
42/49 + (-42/49) = 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: 42/49
- Additive inverse: -42/49
To verify: 42/49 + (-42/49) = 0
Extended Mathematical Exploration of 42/49
Let's explore various mathematical operations and concepts related to 42/49 and its additive inverse -42/49.
Basic Operations and Properties
- Square of 42/49: 0.73469387755102
- Cube of 42/49: 0.62973760932945
- Square root of |42/49|: 0.92582009977255
- Reciprocal of 42/49: 1.1666666666667
- Double of 42/49: 1.7142857142857
- Half of 42/49: 0.42857142857143
- Absolute value of 42/49: 0.85714285714286
Trigonometric Functions
- Sine of 42/49: 0.75597536514673
- Cosine of 42/49: 0.65460006667527
- Tangent of 42/49: 1.1548660069443
Exponential and Logarithmic Functions
- e^42/49: 2.3564184423837
- Natural log of 42/49: -0.15415067982726
Floor and Ceiling Functions
- Floor of 42/49: 0
- Ceiling of 42/49: 1
Interesting Properties and Relationships
- The sum of 42/49 and its additive inverse (-42/49) is always 0.
- The product of 42/49 and its additive inverse is: -1764
- The average of 42/49 and its additive inverse is always 0.
- The distance between 42/49 and its additive inverse on a number line is: 84
Applications in Algebra
Consider the equation: x + 42/49 = 0
The solution to this equation is x = -42/49, which is the additive inverse of 42/49.
Graphical Representation
On a coordinate plane:
- The point (42/49, 0) is reflected across the y-axis to (-42/49, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 42/49 and Its Additive Inverse
Consider the alternating series: 42/49 + (-42/49) + 42/49 + (-42/49) + ...
The sum of this series oscillates between 0 and 42/49, never converging unless 42/49 is 0.
In Number Theory
For integer values:
- If 42/49 is even, its additive inverse is also even.
- If 42/49 is odd, its additive inverse is also odd.
- The sum of the digits of 42/49 and its additive inverse may or may not be the same.
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