21/35 Additive Inverse :
The additive inverse of 21/35 is -21/35.
This means that when we add 21/35 and -21/35, the result is zero:
21/35 + (-21/35) = 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: 21/35
- Additive inverse: -21/35
To verify: 21/35 + (-21/35) = 0
Extended Mathematical Exploration of 21/35
Let's explore various mathematical operations and concepts related to 21/35 and its additive inverse -21/35.
Basic Operations and Properties
- Square of 21/35: 0.36
- Cube of 21/35: 0.216
- Square root of |21/35|: 0.77459666924148
- Reciprocal of 21/35: 1.6666666666667
- Double of 21/35: 1.2
- Half of 21/35: 0.3
- Absolute value of 21/35: 0.6
Trigonometric Functions
- Sine of 21/35: 0.56464247339504
- Cosine of 21/35: 0.82533561490968
- Tangent of 21/35: 0.68413680834169
Exponential and Logarithmic Functions
- e^21/35: 1.8221188003905
- Natural log of 21/35: -0.51082562376599
Floor and Ceiling Functions
- Floor of 21/35: 0
- Ceiling of 21/35: 1
Interesting Properties and Relationships
- The sum of 21/35 and its additive inverse (-21/35) is always 0.
- The product of 21/35 and its additive inverse is: -441
- The average of 21/35 and its additive inverse is always 0.
- The distance between 21/35 and its additive inverse on a number line is: 42
Applications in Algebra
Consider the equation: x + 21/35 = 0
The solution to this equation is x = -21/35, which is the additive inverse of 21/35.
Graphical Representation
On a coordinate plane:
- The point (21/35, 0) is reflected across the y-axis to (-21/35, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 21/35 and Its Additive Inverse
Consider the alternating series: 21/35 + (-21/35) + 21/35 + (-21/35) + ...
The sum of this series oscillates between 0 and 21/35, never converging unless 21/35 is 0.
In Number Theory
For integer values:
- If 21/35 is even, its additive inverse is also even.
- If 21/35 is odd, its additive inverse is also odd.
- The sum of the digits of 21/35 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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