- Chat with library staff now
- Contact your library

Skip to Main Content
# Math: Basic Tutorials : Rearranging Formulas

## Rearranging Formulas

An equation with more than one variable is sometimes called a formula. Formulas show us how the variables are related to one another (e.g. A = LW). This section explains how you can rearrange formulas to isolate for a given variable.

## Examples

## Summary and Worksheet

## Attribution

Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on the titles below to view each example.

Rearrange A equals 2 times l plus 2 times w to isolate for w.

Line 1: We want to get w all by itself on one side of the equation, so we first we have to undo plus 2l by subtracting 2l from both sides, so the equation is A minus 2l equals 2l minus 2l plus 2w.

Line 2: Simplify the equation to A minus 2l equals 2w.

Line 3: To undo the multiplication we divide both sides by 2 so the equation becomes A minus 2l all over 2 equals 2w over 2.

Line 4: Simplify to get A minus 2l all over 2 equals w.

Line 5: Therefore, the equation rearranged for w is w equals A minus 2l all over 2.

Solve for r in the equation A equals P times open bracket 1 plus r t close bracket.

Line 1: We want to get r all by itself on one side of the equation, so first we must remove the brackets by multiplying each term inside the brackets by P. The equation becomes A equals P plus P r t.

Line 2: Remove P on the right side of the equation by subtracting P from both sides so the equation becomes A minus P equals P minus P plus P r t.

Line 3: Simplify the equation to A minus P equals P r t.

Line 4: To isolate for r, we need to undo the multiplication, so we divide both sides by P t, so the equation becomes A minus P all over P t equals P r t over P t.

Line 5: Simplify to get A minus P all over P t equals r

Line 5: Therefore, the equation solved for r is r equals A minus P all over P t.

- Summary: Rearranging Formulas - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Rearranging Formulas - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.