Rearranging formulas: two steps worksheets

Two steps is where order starts to matter. These free printable worksheets take real formulas such as P = 2l + 2w and A = ½bh and ask for a letter that is two operations away, with the working printed on the answer key.

Rearranging formulas: two steps
Rearranging formulas: two steps worksheet — Real formulas, two steps, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Rearranging P = 2l + 2w for l means undoing what was done to l in the opposite order. It was multiplied by 2 and then had 2w added, so 2w comes off first and the 2 goes second. Students who divide first are not wrong, but they then have to divide every term, and that is where the mistakes come from. The key shows P − 2w = 2l, and then (P − 2w)/2 = l.

Why this sheet works

A fraction in front is its own kind of two steps. In A = ½bh the student has to double both sides to get rid of the half, and then divide by the other letter. The Fahrenheit formula takes the 32 off first and only then deals with the fraction. These are formulas from real courses, and a student who has done them will recognize them in science later on.

How this one works

Solve A = ½pq for p

A = ½pq
2A = pq
= p
p =
  1. A = ½pq is the area of a rhombus. To make p the subject, undo everything that is being done to it.
  2. Multiply both sides by 2 to clear the half. A = ½pq becomes 2A = pq.
  3. Divide both sides by what multiplies it. 2A = pq becomes 2A/q = p.
  4. Write it with the letter you want on the left. 2A/q = p becomes p = 2A/q.