How to Solve Literal Equations and Rearrange Formulas

$t$ is multiplied by $r$. Treat $r$ as if it were a number.

$t = \tfrac{d}{r}$

Divide both sides by $r$: $t = \tfrac{d}{r}$.

Check: $r = 60$, $t = 2$ gives $d = 120$; rearranged, $t = \tfrac{120}{60} = 2$ ✓

$r = \tfrac{C}{2\pi}$

$r$ is multiplied by $2\pi$, so divide both sides by $2\pi$: $r = \tfrac{C}{2\pi}$.

$x = \tfrac{y - b}{m}$

Subtract $b$: $y - b = mx$. Divide by $m$: $x = \tfrac{y - b}{m}$, valid when $m \neq 0$.

Clear the fraction first by multiplying both sides by $2$.

$h = \tfrac{2A}{b}$

Multiply both sides by $2$: $2A = bh$. Divide by $b$: $h = \tfrac{2A}{b}$.

Check: $b = 6$, $h = 4$ gives $A = 12$; rearranged, $h = \tfrac{24}{6} = 4$ ✓

$w = \tfrac{P - 2l}{2}$

Subtract $2l$: $P - 2l = 2w$. Divide by $2$: $w = \tfrac{P - 2l}{2}$.

$h = \tfrac{V}{lw}$

$h$ is multiplied by both $l$ and $w$, so divide both sides by $lw$: $h = \tfrac{V}{lw}$.

$x = \tfrac{c - b}{a}$, valid when $a \neq 0$.

Subtract $b$: $ax = c - b$. Divide by $a$: $x = \tfrac{c - b}{a}$.

If $a = 0$ the original equation is $b = c$, which contains no $x$ at all, so dividing by $a$ is not allowed.

Rearrange first, substitute second. That is the whole point of the technique.

$r = \tfrac{I}{Pt}$, and $r = 0.03$, i.e. 3%.

$r$ is multiplied by $P$ and $t$, so divide both sides by $Pt$: $r = \tfrac{I}{Pt}$.

Substituting: $r = \tfrac{120}{2000 \times 2} = \tfrac{120}{4000} = 0.03$.

As a percentage that is $3\%$. Check: $Prt = 2000 \times 0.03 \times 2 = 120$ ✓