42/48 Additive Inverse :
The additive inverse of 42/48 is -42/48.
This means that when we add 42/48 and -42/48, the result is zero:
42/48 + (-42/48) = 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: 42/48
- Additive inverse: -42/48
To verify: 42/48 + (-42/48) = 0
Extended Mathematical Exploration of 42/48
Let's explore various mathematical operations and concepts related to 42/48 and its additive inverse -42/48.
Basic Operations and Properties
- Square of 42/48: 0.765625
- Cube of 42/48: 0.669921875
- Square root of |42/48|: 0.93541434669349
- Reciprocal of 42/48: 1.1428571428571
- Double of 42/48: 1.75
- Half of 42/48: 0.4375
- Absolute value of 42/48: 0.875
Trigonometric Functions
- Sine of 42/48: 0.76754350223603
- Cosine of 42/48: 0.64099685816333
- Tangent of 42/48: 1.1974216292343
Exponential and Logarithmic Functions
- e^42/48: 2.3988752939671
- Natural log of 42/48: -0.13353139262452
Floor and Ceiling Functions
- Floor of 42/48: 0
- Ceiling of 42/48: 1
Interesting Properties and Relationships
- The sum of 42/48 and its additive inverse (-42/48) is always 0.
- The product of 42/48 and its additive inverse is: -1764
- The average of 42/48 and its additive inverse is always 0.
- The distance between 42/48 and its additive inverse on a number line is: 84
Applications in Algebra
Consider the equation: x + 42/48 = 0
The solution to this equation is x = -42/48, which is the additive inverse of 42/48.
Graphical Representation
On a coordinate plane:
- The point (42/48, 0) is reflected across the y-axis to (-42/48, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 42/48 and Its Additive Inverse
Consider the alternating series: 42/48 + (-42/48) + 42/48 + (-42/48) + ...
The sum of this series oscillates between 0 and 42/48, never converging unless 42/48 is 0.
In Number Theory
For integer values:
- If 42/48 is even, its additive inverse is also even.
- If 42/48 is odd, its additive inverse is also odd.
- The sum of the digits of 42/48 and its additive inverse may or may not be the same.
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