10/15 Additive Inverse :
The additive inverse of 10/15 is -10/15.
This means that when we add 10/15 and -10/15, the result is zero:
10/15 + (-10/15) = 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: 10/15
- Additive inverse: -10/15
To verify: 10/15 + (-10/15) = 0
Extended Mathematical Exploration of 10/15
Let's explore various mathematical operations and concepts related to 10/15 and its additive inverse -10/15.
Basic Operations and Properties
- Square of 10/15: 0.44444444444444
- Cube of 10/15: 0.2962962962963
- Square root of |10/15|: 0.81649658092773
- Reciprocal of 10/15: 1.5
- Double of 10/15: 1.3333333333333
- Half of 10/15: 0.33333333333333
- Absolute value of 10/15: 0.66666666666667
Trigonometric Functions
- Sine of 10/15: 0.61836980306974
- Cosine of 10/15: 0.78588726077695
- Tangent of 10/15: 0.78684288947298
Exponential and Logarithmic Functions
- e^10/15: 1.9477340410547
- Natural log of 10/15: -0.40546510810816
Floor and Ceiling Functions
- Floor of 10/15: 0
- Ceiling of 10/15: 1
Interesting Properties and Relationships
- The sum of 10/15 and its additive inverse (-10/15) is always 0.
- The product of 10/15 and its additive inverse is: -100
- The average of 10/15 and its additive inverse is always 0.
- The distance between 10/15 and its additive inverse on a number line is: 20
Applications in Algebra
Consider the equation: x + 10/15 = 0
The solution to this equation is x = -10/15, which is the additive inverse of 10/15.
Graphical Representation
On a coordinate plane:
- The point (10/15, 0) is reflected across the y-axis to (-10/15, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10/15 and Its Additive Inverse
Consider the alternating series: 10/15 + (-10/15) + 10/15 + (-10/15) + ...
The sum of this series oscillates between 0 and 10/15, never converging unless 10/15 is 0.
In Number Theory
For integer values:
- If 10/15 is even, its additive inverse is also even.
- If 10/15 is odd, its additive inverse is also odd.
- The sum of the digits of 10/15 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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