Rearranging an equation can often be very helpful when working in a subject other than math, such as physics, chemistry, carpentry, or baking. If you know every value except for one, substituting the values into one expression and simplifying to find the missing value is a lot faster than solving each time.

Example

Imagine that we were commissioned to paint a mural. We were told that the exact required area

A

of our painting should be

50 ft^{2}

but we were not told how long or wide it should be. We can use the formula for area of a rectangle to play around with various possible dimensions. However, it is much easier to do this with the formula rewritten a little bit.

A = ℓ w \Leftrightarrow ℓ = \frac{A}{w} 50 = ℓ w \Leftrightarrow ℓ = \frac{5 0}{w}

Now we can substitute possible widths into the equation and find the corresponding lengths.

Possible Width	Substitution	Corresponding Length
$w = 10 ft$	$ℓ = \frac{5 0}{1 0}$	$ℓ = 5 ft$
$w = 20 ft$	$ℓ = \frac{5 0}{2 0}$	$ℓ = 2.5 ft$
$w = 30 ft$	$ℓ = \frac{5 0}{3 0}$	$ℓ = 1 . \overset{ˉ}{6} ft$

Exercise

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