Learning Objectives
- Explain what the subject of a formula is.
- Identify the subject of a formula.
- Rearrange simple formulae.
- Use inverse operations correctly.
- Check your rearranged formula.
Introduction
This lesson develops Changing the Subject of a Formula from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
๐ฌ Rearrange without breaking equality
Undo operations in reverse order to isolate the new subject.
๐ค Think About This...
Imagine you're travelling from Harare to Bulawayo. You know:
- ๐ Distance travelled
- โฐ Time taken
But you don't know your speed.
The formula is:
Instead of creating a new formula, we simply rearrange the one we already have.
๐ What is the Subject of a Formula?
The subject of a formula is the letter that is alone on one side of the equals sign.
The subject is A because it stands by itself.
๐ง Did You Notice?
Solving an equation finds the value of a variable.
Changing the subject rearranges the formula without finding a value.
๐ง The StudyNest Thinking Method
๐ Which letter am I trying to leave alone?
Every step you perform should help isolate that letter.
๐ Worked Examples
Example 1
Make x the subject.
๐ StudyNest Question: Which letter must stand alone?
We want x by itself.
Subtract 5 from both sides.
Write the subject first.
Example 2
Make m the subject.
Divide both sides by 4.
Example 3
Make b the subject.
Add 9 to both sides.
Example 4
Make t the subject.
๐ StudyNest Question: Which letter are we trying to leave on its own?
We want t by itself.
Since t is multiplied by s, divide both sides by s.
Example 5
Make w the subject.
Since w is multiplied by l, divide both sides by l.
๐ Real-Life Example
The formula for the area of a rectangle is:
If the area is 24 cmยฒ and the width is 6 cm, find the length.
First rearrange the formula.
Now substitute the values.
โ Common Mistakes
Forgetting which letter should become the subject.
Doing different operations on each side of the formula. Remember, whatever you do to one side, you must also do to the other.
Stopping before the required letter is completely by itself.
Leaving the new subject on the right-hand side. It is good mathematical practice to write the subject on the left.
Practice Questions
Make the letter shown the subject.
-
y = x + 8
Make x the subject. -
P = 7m
Make m the subject. -
A = lw
Make l the subject. -
d = st
Make s the subject. -
C = 2ฯr
Make r the subject.
โ Show Answers
- x = y โ 8
- m = P/7
- l = A/w
- s = d/t
- r = C/2ฯ
๐ง Did You Know?
โญ What You Can Do Now
- โ I know what the subject of a formula is.
- โ I can identify the subject.
- โ I can use inverse operations to rearrange formulae.
- โ I can write the new subject on the left.
- โ I understand the difference between solving an equation and changing the subject.
๐ Well Done!
You can now rearrange simple formulae with confidence. Remember to focus on one question:
๐ง Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
๐ Your Progress
Lesson 11 of 22
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.