3/4 Additive Inverse :
The additive inverse of 3/4 is -3/4.
This means that when we add 3/4 and -3/4, the result is zero:
3/4 + (-3/4) = 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: 3/4
- Additive inverse: -3/4
To verify: 3/4 + (-3/4) = 0
Extended Mathematical Exploration of 3/4
Let's explore various mathematical operations and concepts related to 3/4 and its additive inverse -3/4.
Basic Operations and Properties
- Square of 3/4: 0.5625
- Cube of 3/4: 0.421875
- Square root of |3/4|: 0.86602540378444
- Reciprocal of 3/4: 1.3333333333333
- Double of 3/4: 1.5
- Half of 3/4: 0.375
- Absolute value of 3/4: 0.75
Trigonometric Functions
- Sine of 3/4: 0.68163876002333
- Cosine of 3/4: 0.73168886887382
- Tangent of 3/4: 0.93159645994407
Exponential and Logarithmic Functions
- e^3/4: 2.1170000166127
- Natural log of 3/4: -0.28768207245178
Floor and Ceiling Functions
- Floor of 3/4: 0
- Ceiling of 3/4: 1
Interesting Properties and Relationships
- The sum of 3/4 and its additive inverse (-3/4) is always 0.
- The product of 3/4 and its additive inverse is: -9
- The average of 3/4 and its additive inverse is always 0.
- The distance between 3/4 and its additive inverse on a number line is: 6
Applications in Algebra
Consider the equation: x + 3/4 = 0
The solution to this equation is x = -3/4, which is the additive inverse of 3/4.
Graphical Representation
On a coordinate plane:
- The point (3/4, 0) is reflected across the y-axis to (-3/4, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 3/4 and Its Additive Inverse
Consider the alternating series: 3/4 + (-3/4) + 3/4 + (-3/4) + ...
The sum of this series oscillates between 0 and 3/4, never converging unless 3/4 is 0.
In Number Theory
For integer values:
- If 3/4 is even, its additive inverse is also even.
- If 3/4 is odd, its additive inverse is also odd.
- The sum of the digits of 3/4 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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