Solving for a Letter
Part of the Fundamentals section of Coddy's Math journey. Lesson 58 of 64.
Sometimes you want a formula rearranged, permanently, for a different letter. From P = 2l + 2w, make a formula for w. Treat every other letter as if it were a known number and undo the layers around w: subtract 2l from both sides, then divide by 2.
P - 2l = 2w
w = (P - 2l)/2
That is a formula for the width in terms of the perimeter and the length. It is the same equation, solved for w instead of P.
Nothing here needs numbers. The steps are the ones you know; the only new habit is reading letters like P and l as "some number we are not told" and moving them out of the way like any number. Scientists and engineers do this all day.
Challenge
Rearrange d = st to give a formula for the time t.
Try it yourself
Solve for t
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Fundamentals
1What an Equation Is
The EquationFinding the UnknownThe Same to Both SidesSolved Means AloneRecap: First Equations4Two-Step Equations
Two Layers to UndoSubtract, Then DivideAdd, Then DivideA Division InsideNegatives in Two StepsRecap: Two-Step Equations2One-Step Equations
Undoing AdditionUndoing SubtractionUndoing MultiplicationUndoing DivisionInverse OperationsRecap: One-Step Equations5Tidying First
Like TermsTerms and Numbers MixedThe Distributive PropertyDistributing a SubtractionTidy, Then SolveRecap: Tidying First