# Balancing equations

1. Apr 17, 2007

### Ry122

in f=v/a
i want to divide f/2. What do i change on the other side
of the equation? I need to determine a

2. Apr 17, 2007

### Gib Z

I am confused, what do you want to do to it? Do you want f/2 on one side?

f= v/a

Divide both sides by 2.
f/2 = v/(2a)

3. Apr 17, 2007

### Gib Z

O and as for determining a, im lost as well, as to what you mean.

f=v/a
fa=v
a=v/f

4. Apr 17, 2007

### VietDao29

One basic rule in manipulating equations is to remember that what you do to one side of an equation, do exactly to the other side as well.

So, here we go:
$$f = \frac{v}{a}$$
If we want to have f/2, i.e, we have to divide the LHS by 2, right? So, we should also divide the RHS by 2, like this:
$$\frac{f}{2} = \frac{\frac{v}{a}}{2} = \frac{v}{2a}$$

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Now, say we want to solve for a, we will try to isolate a to one side of the equation, like this:

$$f = \frac{v}{a}$$

Multiply both sides by a to obtain:

$$\Rightarrow fa = \frac{v}{a} \times a = v$$

The LHS has fa, and we want it to be a, so we divide both sides by f, and arrive at:

$$\Rightarrow \frac{fa}{f} = \frac{v}{f}$$

$$\Rightarrow a = \frac{v}{f}$$