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All courses Math I · A-CED.4 4 of 59
Rearrange formulas to isolate a chosen quantity and interpret the result.

Rearrange a formula by dividing to isolate the target

Problem
Rearrange F = ma to solve for a. State any restriction.
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Hint

Divide both sides of F = ma by m to isolate a.

When solving F = ma for a, m cannot be 0 because division by 0 is undefined.

Solution walkthrough

01

Start with the formula

\[F~=~\text{ma}\]

The target variable a is multiplied by m, so the inverse operation will be division by m.

02

Divide both sides by m

\[F~/~m~=~\text{ma}~/~m\]

Dividing both sides by the same nonzero quantity keeps the formula equivalent and begins isolating a.

03

Simplify

\[a~=~F~/~m\]

The factor m cancels on the right, leaving a by itself.

04

State the formula and restriction

\[\text{restriction}:~m~\ne~0;~a~=~F/m\]

Because the solving step divided by m, m cannot equal 0. The rearranged formula is a = F/m with that restriction.

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Another way

  1. You can check by substituting a = F/m back into F = ma to get F = m(F/m) = F.

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Common mistake

A common mistake is to state only a = F/m and forget the restriction that m must be nonzero.