Parallel Addition

Parallel Addition[2,3]=1.2

In a physics class, you will learn that there are two forms of addition.

2+3=?

The type of Addition that you learned, probably even before getting to grade school, is called Serial Addition, and it is shown below:

$a + b = c$

The other type of Addition is Parallel Addition:

$\dfrac{1}{a} + \dfrac{1}{b} = \dfrac{1}{c}$

We can use algebra to solve for c. First we work to bring the two terms on the left side together. We need for them to have the same denominator:

$\dfrac{b}{b}\dfrac{1}{a} + \dfrac{a}{a}\dfrac{1}{b} = \dfrac{1}{c}$ $\dfrac{b}{ab} + \dfrac{a}{ab} = \dfrac{1}{c}$ $\dfrac{a + b}{ab} = \dfrac{1}{c}$

We can now use the trick of moving a factor from one side of the equation to the other–a denominator jumps to the numerator and a numerator jumps to the denominator:

$\dfrac{c}{ab} = \dfrac{1}{a+b}$ $c = \dfrac{ab}{a+b}$

If we use this with the numbers 2 and 3 for a and b then we get the following:

$\dfrac {(2)(3)}{2+3}=\dfrac{6}{5} = 1.2$

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