45/60 Additive Inverse :
The additive inverse of 45/60 is -45/60.
This means that when we add 45/60 and -45/60, the result is zero:
45/60 + (-45/60) = 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: 45/60
- Additive inverse: -45/60
To verify: 45/60 + (-45/60) = 0
Extended Mathematical Exploration of 45/60
Let's explore various mathematical operations and concepts related to 45/60 and its additive inverse -45/60.
Basic Operations and Properties
- Square of 45/60: 0.5625
- Cube of 45/60: 0.421875
- Square root of |45/60|: 0.86602540378444
- Reciprocal of 45/60: 1.3333333333333
- Double of 45/60: 1.5
- Half of 45/60: 0.375
- Absolute value of 45/60: 0.75
Trigonometric Functions
- Sine of 45/60: 0.68163876002333
- Cosine of 45/60: 0.73168886887382
- Tangent of 45/60: 0.93159645994407
Exponential and Logarithmic Functions
- e^45/60: 2.1170000166127
- Natural log of 45/60: -0.28768207245178
Floor and Ceiling Functions
- Floor of 45/60: 0
- Ceiling of 45/60: 1
Interesting Properties and Relationships
- The sum of 45/60 and its additive inverse (-45/60) is always 0.
- The product of 45/60 and its additive inverse is: -2025
- The average of 45/60 and its additive inverse is always 0.
- The distance between 45/60 and its additive inverse on a number line is: 90
Applications in Algebra
Consider the equation: x + 45/60 = 0
The solution to this equation is x = -45/60, which is the additive inverse of 45/60.
Graphical Representation
On a coordinate plane:
- The point (45/60, 0) is reflected across the y-axis to (-45/60, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 45/60 and Its Additive Inverse
Consider the alternating series: 45/60 + (-45/60) + 45/60 + (-45/60) + ...
The sum of this series oscillates between 0 and 45/60, never converging unless 45/60 is 0.
In Number Theory
For integer values:
- If 45/60 is even, its additive inverse is also even.
- If 45/60 is odd, its additive inverse is also odd.
- The sum of the digits of 45/60 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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