35/42 Additive Inverse :
The additive inverse of 35/42 is -35/42.
This means that when we add 35/42 and -35/42, the result is zero:
35/42 + (-35/42) = 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: 35/42
- Additive inverse: -35/42
To verify: 35/42 + (-35/42) = 0
Extended Mathematical Exploration of 35/42
Let's explore various mathematical operations and concepts related to 35/42 and its additive inverse -35/42.
Basic Operations and Properties
- Square of 35/42: 0.69444444444444
- Cube of 35/42: 0.5787037037037
- Square root of |35/42|: 0.91287092917528
- Reciprocal of 35/42: 1.2
- Double of 35/42: 1.6666666666667
- Half of 35/42: 0.41666666666667
- Absolute value of 35/42: 0.83333333333333
Trigonometric Functions
- Sine of 35/42: 0.74017685319604
- Cosine of 35/42: 0.67241224408306
- Tangent of 35/42: 1.1007783687898
Exponential and Logarithmic Functions
- e^35/42: 2.3009758908928
- Natural log of 35/42: -0.18232155679395
Floor and Ceiling Functions
- Floor of 35/42: 0
- Ceiling of 35/42: 1
Interesting Properties and Relationships
- The sum of 35/42 and its additive inverse (-35/42) is always 0.
- The product of 35/42 and its additive inverse is: -1225
- The average of 35/42 and its additive inverse is always 0.
- The distance between 35/42 and its additive inverse on a number line is: 70
Applications in Algebra
Consider the equation: x + 35/42 = 0
The solution to this equation is x = -35/42, which is the additive inverse of 35/42.
Graphical Representation
On a coordinate plane:
- The point (35/42, 0) is reflected across the y-axis to (-35/42, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 35/42 and Its Additive Inverse
Consider the alternating series: 35/42 + (-35/42) + 35/42 + (-35/42) + ...
The sum of this series oscillates between 0 and 35/42, never converging unless 35/42 is 0.
In Number Theory
For integer values:
- If 35/42 is even, its additive inverse is also even.
- If 35/42 is odd, its additive inverse is also odd.
- The sum of the digits of 35/42 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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