31/35 Additive Inverse :
The additive inverse of 31/35 is -31/35.
This means that when we add 31/35 and -31/35, the result is zero:
31/35 + (-31/35) = 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: 31/35
- Additive inverse: -31/35
To verify: 31/35 + (-31/35) = 0
Extended Mathematical Exploration of 31/35
Let's explore various mathematical operations and concepts related to 31/35 and its additive inverse -31/35.
Basic Operations and Properties
- Square of 31/35: 0.78448979591837
- Cube of 31/35: 0.69483381924198
- Square root of |31/35|: 0.94112394811432
- Reciprocal of 31/35: 1.1290322580645
- Double of 31/35: 1.7714285714286
- Half of 31/35: 0.44285714285714
- Absolute value of 31/35: 0.88571428571429
Trigonometric Functions
- Sine of 31/35: 0.77436713930825
- Cosine of 31/35: 0.63273654356261
- Tangent of 31/35: 1.2238381790756
Exponential and Logarithmic Functions
- e^31/35: 2.4247157128778
- Natural log of 31/35: -0.12136085700427
Floor and Ceiling Functions
- Floor of 31/35: 0
- Ceiling of 31/35: 1
Interesting Properties and Relationships
- The sum of 31/35 and its additive inverse (-31/35) is always 0.
- The product of 31/35 and its additive inverse is: -961
- The average of 31/35 and its additive inverse is always 0.
- The distance between 31/35 and its additive inverse on a number line is: 62
Applications in Algebra
Consider the equation: x + 31/35 = 0
The solution to this equation is x = -31/35, which is the additive inverse of 31/35.
Graphical Representation
On a coordinate plane:
- The point (31/35, 0) is reflected across the y-axis to (-31/35, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 31/35 and Its Additive Inverse
Consider the alternating series: 31/35 + (-31/35) + 31/35 + (-31/35) + ...
The sum of this series oscillates between 0 and 31/35, never converging unless 31/35 is 0.
In Number Theory
For integer values:
- If 31/35 is even, its additive inverse is also even.
- If 31/35 is odd, its additive inverse is also odd.
- The sum of the digits of 31/35 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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