In this lesson:
By the end of this lesson, you will be able to:
From (Ohm's Law), rearrange for any variable:
One formula — three tools
The steps are identical — letters play the role of "known" quantities:
Numeric equation:
Formula rearrangement (same moves):
Same two inverse operations — same logic as the numeric case
For , solving for :
Why can we treat and as constants while solving for ?
Think: what would the numeric equivalent look like?
Apply inverse operations to isolate the target
Undo one operation to isolate the target variable:
Rule: Last operation applied → first operation undone
Divide or multiply first, then add or subtract — as needed
Treat , , , , , as constants — divide both sides by the product
Rearrange each formula for the indicated variable:
Write the rearranged formula before checking the answer
Each answer is a formula itself — use it for any values of the other variables
When the target appears in multiple terms, factor it out first:
1. appears in two terms — factor:
2. Divide both sides by :
1. Isolate :
2. Take the square root ():
Take the square root last — after isolating
For , a student writes:
Is this step correct? Explain.
Then: What should the student do next?
Solve for :
Hint: Isolate first by moving the other term.
Write each step before the answer
Rearrange each for the indicated variable:
Ask: What do you know? What do you need?
Problem 1: A 100 m race completed in 9.58 s. Find average speed.
Problem 2: Cylinder: cm³, cm. Find height .
Problem: 500 grew to 650 in 3 years (simple interest). Find annual rate .
Units: dollars / (dollars · years) = 1/year — rate is per year ✓
For each problem, identify the formula, rearrange it, then substitute:
A 400-meter swim completed in 250 seconds. Find average speed.
A simple-interest loan: $800 borrowed, $72 interest, rate = 6%. Find the time.
Identify which variable to solve for before computing
✓ Rearranging = equation solving with letters as constants
✓ Undo operations in reverse order (last applied → first undone)
Target in multiple terms? Factor it out before dividing
Target squared? Isolate the power, then take the root last
Apply every operation to the entire other side
This skill appears across all of math and science:
Rearrange once — reuse the form for every future problem.
Click to begin the narrated lesson
Rearrange formulas