70/80 Additive Inverse :
The additive inverse of 70/80 is -70/80.
This means that when we add 70/80 and -70/80, the result is zero:
70/80 + (-70/80) = 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: 70/80
- Additive inverse: -70/80
To verify: 70/80 + (-70/80) = 0
Extended Mathematical Exploration of 70/80
Let's explore various mathematical operations and concepts related to 70/80 and its additive inverse -70/80.
Basic Operations and Properties
- Square of 70/80: 0.765625
- Cube of 70/80: 0.669921875
- Square root of |70/80|: 0.93541434669349
- Reciprocal of 70/80: 1.1428571428571
- Double of 70/80: 1.75
- Half of 70/80: 0.4375
- Absolute value of 70/80: 0.875
Trigonometric Functions
- Sine of 70/80: 0.76754350223603
- Cosine of 70/80: 0.64099685816333
- Tangent of 70/80: 1.1974216292343
Exponential and Logarithmic Functions
- e^70/80: 2.3988752939671
- Natural log of 70/80: -0.13353139262452
Floor and Ceiling Functions
- Floor of 70/80: 0
- Ceiling of 70/80: 1
Interesting Properties and Relationships
- The sum of 70/80 and its additive inverse (-70/80) is always 0.
- The product of 70/80 and its additive inverse is: -4900
- The average of 70/80 and its additive inverse is always 0.
- The distance between 70/80 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/80 = 0
The solution to this equation is x = -70/80, which is the additive inverse of 70/80.
Graphical Representation
On a coordinate plane:
- The point (70/80, 0) is reflected across the y-axis to (-70/80, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/80 and Its Additive Inverse
Consider the alternating series: 70/80 + (-70/80) + 70/80 + (-70/80) + ...
The sum of this series oscillates between 0 and 70/80, never converging unless 70/80 is 0.
In Number Theory
For integer values:
- If 70/80 is even, its additive inverse is also even.
- If 70/80 is odd, its additive inverse is also odd.
- The sum of the digits of 70/80 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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