Literal Equations and Formulas
Rearrange a formula to solve for a chosen variable.
About this topic
A literal equation contains several letters, and you rearrange it to solve for one of them. Formulas such as area A = lw, distance d = rt or the temperature conversion F = 9C/5 + 32 are literal equations. You use the same inverse operations as with numbers, treating the other letters as if they were numbers.
Rearranging a formula once is faster than recalculating every time. For example, from d = rt you can get r = d/t to find speed directly, which is essential in science and engineering. To solve F = 9C/5 + 32 for C, subtract 32 to get F − 32 = 9C/5, multiply by 5/9 and obtain C = 5(F − 32)/9.
Consider the perimeter of a rectangle, P = 2l + 2w. If you know P and l and want the width, subtract 2l and divide by 2: w = (P − 2l)/2. A rectangular garden with perimeter 30 and length 9 therefore has width (30 − 18)/2 = 6. Simple interest I = Prt can be rearranged to find the time or rate.
A typical error is dividing only one term instead of the whole side, such as turning 2w = P − 2l into w = P − l instead of w = (P − 2l)/2. Another is being unsettled by letters. Remember that the steps are exactly those you would use with numbers, so try the problem with simple numbers first if you are stuck.
Key ideas
- Treat other letters as numbers
- Use inverse operations
- Common in physics and geometry
Quick check
Use cases: where Literal Equations and Formulas helps
- Homework: review the key idea behind Literal Equations and Formulas before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Literal Equations and Formulas without notes.
- Visual learning: play with the interactive lab to see how Literal Equations and Formulas changes when you adjust its inputs.
- Teaching a friend: explain Literal Equations and Formulas in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Literal Equations and Formulas?
Rearrange a formula to solve for a chosen variable.
What will I learn in Literal Equations and Formulas?
Treat other letters as numbers. Use inverse operations. Common in physics and geometry.
Is Literal Equations and Formulas part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Literal Equations and Formulas lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Literal Equations and Formulas?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.