Did you know? A student can use a formula correctly when every value is supplied, then freeze when the question asks for a different letter. Nothing mysterious has happened. The same relationship is being read from the other direction.
Quick answer for Bukit Timah parents: changing the subject of a formula means rearranging a correct equation so that the requested variable stands alone on one side. In G1 Mathematics, success comes from balancing operations, keeping brackets intact, checking units and substituting back into the original formula.
What does it mean to make a letter the subject?
Take the rectangular perimeter formula P = 2(L + W), where P is the perimeter and L and W are length and width. P is currently the subject because it stands alone on the left. If we need W, we must rearrange the same equation rather than learn a new geometry formula.
Example 1: make the width the subject
Begin with P = 2(L + W). Divide both sides by 2: P/2 = L + W. Subtract L from both sides: W = P/2 − L. This equation now gives the width directly.
Suppose the perimeter is 38 cm and the length is 12 cm. Substitute W = 38/2 − 12 = 19 − 12 = 7 cm. Check: 2(12 + 7) = 38 cm. The check matters because it catches an incorrect bracket or division.
Example 2: a box’s height is the unknown
For a rectangular box, V = L × W × H. To make H the subject, divide both sides by the product LW: H = V/(LW).
If V = 1,200 cm³, L = 20 cm and W = 10 cm, then H = 1,200/(20 × 10) = 6 cm. The volume is measured in cubic centimetres, while the answer is a length in centimetres. A student can use that difference to see whether the units make sense.
The calculation assumes L and W are non-zero. It also assumes the measurements are the internal dimensions if the question is about capacity.
Example 3: finding how many items were bought
Imagine an illustrative receipt with a fixed $7 service fee and items costing $5 each. The model is C = 5n + 7, where C is total cost in dollars and n is the number of items.
Make n the subject: first subtract 7 to get C − 7 = 5n. Then divide by 5: n = (C − 7)/5. With C = $42, n = (42 − 7)/5 = 7 items.
This is also why brackets matter. Entering 42 − 7 ÷ 5 in a calculator without brackets calculates a different expression. A tutor should ask the learner to speak the operation order before pressing a key.
The balance method is better than ‘moving’ numbers
Students sometimes learn a shortcut such as “move the 7 across and change its sign”. That can work in a simple example but may become confusing when the formula includes brackets or fractions. More reliably, describe what happens to both sides: subtract 7 from both sides; divide both sides by 5.
- Start: circle the letter you want alone.
- Undo additions or subtractions: apply the inverse operation to both sides.
- Undo multiplication or division: keep brackets around a complete numerator or denominator.
- Preserve equality: do the same valid operation on each side.
- Verify: substitute a small test value into the original formula.
Where does this sit in the official G1 scope?
The SEAB 2027 K110 Mathematics syllabus includes changing the subject of a simple formula and finding the value of an unknown quantity from a given formula in its N5 Algebraic expressions and formulae section. The syllabus also connects algebra with practical contexts. The worked examples here are original practice questions, not past-paper items.
A note about examination years: the SEAB 2027 G1 subject list identifies Mathematics as K110, with 4046 given as the reference code for 2026 and earlier. If your child is taking an examination in 2026, follow their actual registered syllabus. The worked questions here are original illustrations, not official examination questions.
A five-minute home check
Ask your child to rearrange A = bh to make b the subject. The answer is b = A/h when h is non-zero. Then try T = 4x + 9 to make x the subject; the answer is x = (T − 9)/4. If the learner can explain each inverse operation without being told the first step, understanding is improving.
Close feedback can help distinguish an algebra difficulty from poor question reading. The unchanged eduKateSG Clementi small-group Mathematics reference describes a three-pupil teaching approach for Secondary 1; ask directly about actual Secondary 4 G1 availability and arrangements.
Frequently asked questions
Is formula rearrangement part of G1? Yes. The 2027 K110 syllabus explicitly includes simple rearrangement.
Should my child memorise a new formula for every unknown? No. Learn to derive it from a correct original formula, then check.
Why do marks disappear even with a calculator? A calculator cannot repair a wrongly rearranged equation or a missing pair of brackets.
Continue learning
Related guides include algebra mistake repair, mensuration and units and simultaneous equations in real life.