All courses Algebra I · A-CED.4 4 of 76
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 \(a\), and state the required 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

Identify the operation on the target

\[F=ma;~a~\text{is}~\text{multiplied}~by~m\]

Treat F and m as the other quantities. Isolating a requires undoing multiplication by m with division.

02

State the division condition

\[\text{division}~by~m~\text{requires}~m\ne~0\]

The inverse operation is valid only when m is nonzero; this is the restriction requested by the prompt.

03

Divide both sides and simplify

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

Dividing both sides by the same nonzero m preserves equality, and the factor m cancels from ma.

04

Check and state the result

\[m(F/m)=F;~m~\ne~0;~a~=~F/m\]

Substituting the solved expression for a returns the original left side. The formula and restriction exactly match choice A.

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Another way

  1. Use the multiplication fact family: if F is the product of m and a, then the missing factor a is product F divided by the known nonzero factor m.

!

Common mistake

Do not omit m != 0. Although a = F/m is algebraically arranged correctly, the division used to obtain it is undefined when m is zero.

Solution walkthrough video