35/49 Additive Inverse :
The additive inverse of 35/49 is -35/49.
This means that when we add 35/49 and -35/49, the result is zero:
35/49 + (-35/49) = 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: 35/49
- Additive inverse: -35/49
To verify: 35/49 + (-35/49) = 0
Extended Mathematical Exploration of 35/49
Let's explore various mathematical operations and concepts related to 35/49 and its additive inverse -35/49.
Basic Operations and Properties
- Square of 35/49: 0.51020408163265
- Cube of 35/49: 0.36443148688047
- Square root of |35/49|: 0.84515425472852
- Reciprocal of 35/49: 1.4
- Double of 35/49: 1.4285714285714
- Half of 35/49: 0.35714285714286
- Absolute value of 35/49: 0.71428571428571
Trigonometric Functions
- Sine of 35/49: 0.65507789717852
- Cosine of 35/49: 0.7555613467007
- Tangent of 35/49: 0.8670082185107
Exponential and Logarithmic Functions
- e^35/49: 2.0427270702661
- Natural log of 35/49: -0.33647223662121
Floor and Ceiling Functions
- Floor of 35/49: 0
- Ceiling of 35/49: 1
Interesting Properties and Relationships
- The sum of 35/49 and its additive inverse (-35/49) is always 0.
- The product of 35/49 and its additive inverse is: -1225
- The average of 35/49 and its additive inverse is always 0.
- The distance between 35/49 and its additive inverse on a number line is: 70
Applications in Algebra
Consider the equation: x + 35/49 = 0
The solution to this equation is x = -35/49, which is the additive inverse of 35/49.
Graphical Representation
On a coordinate plane:
- The point (35/49, 0) is reflected across the y-axis to (-35/49, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 35/49 and Its Additive Inverse
Consider the alternating series: 35/49 + (-35/49) + 35/49 + (-35/49) + ...
The sum of this series oscillates between 0 and 35/49, never converging unless 35/49 is 0.
In Number Theory
For integer values:
- If 35/49 is even, its additive inverse is also even.
- If 35/49 is odd, its additive inverse is also odd.
- The sum of the digits of 35/49 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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