Lesson 6: Changing the Subject of a Formula

👨🏽‍🏫 Introduction

Have you ever used a formula like to find the area of a rectangle? What if you already know the area and the width, and need to find the length?

To do that, you need to make L the subject of the formula — that means rewriting the formula to isolate L. This skill is useful in many areas of math, science, and everyday problem-solving.

By the end of this lesson, you’ll be able to:

• Understand what it means to change the subject of a formula
• Rearrange simple and multi-step formulas
• Apply this skill in real-life scenarios like speed, cost, and geometry problems

🧠 Key Concepts

📌 1. What Does “Changing the Subject” Mean?

Changing the subject means rearranging a formula so that a different variable is isolated (by itself) on one side of the equation.

Example:

From , to make L the subject, divide both sides by W:

🛠️ 2. Rules for Changing the Subject

1. Do the same operation to both sides
2. Use inverse operations (e.g. divide if the subject is being multiplied)
3. Work step-by-step until the desired variable is alone

⚠️ 3. Watch Out For:

• Brackets – expand or factor carefully
• Fractions – multiply or divide wisely
• More than one occurrence of the subject – isolate all terms with the subject first

🧮 Sample Problem Walkthroughs

1. Make x the subject:
   Step 1: Subtract 3 →
   Step 2: Divide by 2 →
2. Make t the subject:
   Step 1: Multiply both sides by t →
   Step 2: Divide by s →
3. Make r the subject:
   Step 1: Divide both sides by →
4. Make y the subject:
   Step 1: Add 2x →
   Step 2: Divide by 3 →
5. Make a the subject:
   Step 1: Multiply both sides by 2 →
   Step 2: Divide both sides by h →
   Step 3: Subtract b →

✍🏽 Practice Exercises

🅰️ A. Change the subject of each formula:

1. Make x the subject:
2. Make r the subject:
3. Make v the subject:
4. Make a the subject:

✅ Answers and Explanations

• 1. Add 2 → , then divide by 5 →
• 2. Divide by π → , then take square root →
• 3. Subtract → , then divide by t →
• 4. Subtract → , then divide by 2s →

📌 Recap

• ✅ Changing the subject means isolating a specific variable
• ✅ Use inverse operations to “undo” steps
• ✅ Always perform the same operation on both sides

💭 Reflection Prompt

Have you seen or used a formula in science or daily life — maybe for area, speed, or budgeting? Try changing the subject of that formula to solve a different part of the problem. For example, if , how would you solve for time?