S4 Mathematics - Term 1

Topic 2: Equations and Inequalities

Lesson 3: Introduction to Changing the Subject

Duration: 40 minutes

Learning Outcomes

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

• Understand what "changing the subject" means
• Rearrange simple formulas with one operation
• Apply inverse operations to isolate a variable

Familiar Formulas

Area of rectangle: A = lw
Perimeter: P = 2l + 2w
Speed: s = d/t

What is the subject in each formula?

The Subject of a Formula

The subject is the variable that stands alone on one side

• In A = lw, the subject is A
• In P = 2l + 2w, the subject is P
• In s = d/t, the subject is s

The Problem

What if we know the area (A) and width (w), but need to find the length (l)?

We need to make l the subject instead of A

This is called "changing the subject"

Inverse Operations

To change the subject, we use inverse (opposite) operations

The Key Principle

Whatever you do to one side, do to the other side

This keeps the equation balanced

Example 1: Addition

Formula: y = x + 5

Make x the subject

x is being added to 5, so subtract 5 from both sides

y - 5 = x + 5 - 5
y - 5 = x

x = y - 5

Example 2: Multiplication

Formula: A = lw (area of rectangle)

Make l the subject

l is being multiplied by w, so divide by w

A ÷ w = lw ÷ w
A/w = l

l = A/w

Example 3: Division

Formula: s = d/t (speed)

Make d the subject

d is being divided by t, so multiply by t

s × t = (d/t) × t
st = d

d = st

Example 4: Subtraction

Formula: C = F - 10

Make F the subject

10 is being subtracted from F, so add 10

C + 10 = F - 10 + 10
C + 10 = F

F = C + 10

The Process

1. Identify the current subject
2. Identify the variable you want as the new subject
3. Identify what operation connects them
4. Apply the inverse operation to both sides

Pair Practice

Make the indicated variable the subject:

1. b = a + 7 (make a the subject)
2. y = 3x (make x the subject)
3. d = vt (make t the subject)

Answers

1. b = a + 7 → a = b - 7
   (subtract 7 from both sides)

2. y = 3x → x = y/3
   (divide both sides by 3)

3. d = vt → t = d/v
   (divide both sides by v)

Checking Your Answer

Original: A = lw

Rearranged: l = A/w

Check with numbers:
If A = 20 and w = 4, then l = 20/4 = 5 ✓
Check: 5 × 4 = 20 = A ✓

Summary

To change the subject:

1. Find the operation connecting variables
2. Use the inverse operation
3. Apply to both sides

Inverse pairs:

• − and × ÷

Exit Questions

Make the indicated variable the subject:

1. y = x + 9 (make x the subject)
2. P = 4s (make s the subject)
3. v = u + at (make u the subject)

Answers

1. y = x + 9 → x = y - 9

2. P = 4s → s = P/4

3. v = u + at → u = v - at

Homework

Make the indicated variable the subject:

1. y = x - 4 (make x)
2. C = 2πr (make r)
3. I = PRT (make P)
4. v = u + at (make a)
5. A = bh (make h)

Next Lesson

Lesson 4: Complex Subject Changes

We will work with:

• Two-step rearrangements
• Formulas with squares and roots
• More complex formulas

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda