70/84 Additive Inverse :
The additive inverse of 70/84 is -70/84.
This means that when we add 70/84 and -70/84, the result is zero:
70/84 + (-70/84) = 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: 70/84
- Additive inverse: -70/84
To verify: 70/84 + (-70/84) = 0
Extended Mathematical Exploration of 70/84
Let's explore various mathematical operations and concepts related to 70/84 and its additive inverse -70/84.
Basic Operations and Properties
- Square of 70/84: 0.69444444444444
- Cube of 70/84: 0.5787037037037
- Square root of |70/84|: 0.91287092917528
- Reciprocal of 70/84: 1.2
- Double of 70/84: 1.6666666666667
- Half of 70/84: 0.41666666666667
- Absolute value of 70/84: 0.83333333333333
Trigonometric Functions
- Sine of 70/84: 0.74017685319604
- Cosine of 70/84: 0.67241224408306
- Tangent of 70/84: 1.1007783687898
Exponential and Logarithmic Functions
- e^70/84: 2.3009758908928
- Natural log of 70/84: -0.18232155679395
Floor and Ceiling Functions
- Floor of 70/84: 0
- Ceiling of 70/84: 1
Interesting Properties and Relationships
- The sum of 70/84 and its additive inverse (-70/84) is always 0.
- The product of 70/84 and its additive inverse is: -4900
- The average of 70/84 and its additive inverse is always 0.
- The distance between 70/84 and its additive inverse on a number line is: 140
Applications in Algebra
Consider the equation: x + 70/84 = 0
The solution to this equation is x = -70/84, which is the additive inverse of 70/84.
Graphical Representation
On a coordinate plane:
- The point (70/84, 0) is reflected across the y-axis to (-70/84, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 70/84 and Its Additive Inverse
Consider the alternating series: 70/84 + (-70/84) + 70/84 + (-70/84) + ...
The sum of this series oscillates between 0 and 70/84, never converging unless 70/84 is 0.
In Number Theory
For integer values:
- If 70/84 is even, its additive inverse is also even.
- If 70/84 is odd, its additive inverse is also odd.
- The sum of the digits of 70/84 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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