Make x the subject of y = 3x − 18: x = (y + □)/□ Fill in each blank

18, 3. Add 18 to both sides: y + 18 = 3x; divide both by 3: x = (y + 18)/3.

Which is the formula S = 6(m − t) with t as its subject? A. t = S/6 − m B. t = m − S/6 C. t = (m − S)/6 D. t = m − 6S Choose the right answer

B. t = m − S/6. Divide both sides by 6: S/6 = m − t; then move the terms: t = m − S/6.

Make x the subject of y = 20 − 5x: x = (□ − y)/□ Fill in each blank

20, 5. Move 5x to the left and y to the right: 5x = 20 − y; divide by 5: x = (20 − y)/5.

Formulae & algebraic fractions · Ages 13–14

Changing the subject of a formula

Treat the new subject as the unknown; do the same to both sides.

How to do it

Method

Treat the new subject as the unknown; do the same to both sides

v = u + at: v − u = at, a = v − ut

Another way

Work backwards

Undo × t, + u: − u, then ÷ t

In full

A formula's subject is the letter alone on one side of it: in v = u + at, it is v. To make a the subject, treat a as the unknown and solve, doing the same to both sides to move the other letters away one at a time: take u from both, v − u = at; divide both by t, a = v − ut. Or work backwards: a is times t, then plus u, to make v; so from v take u, then divide by t. Check with numbers: with u = 6, a = 6 and t = 4, v = 30, and 30 − 64 = 6.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Make x the subject of y = 3x − 18: x = y +
Fill in each blank
Show the answer and working
Answer: 18, 3
Add 18 to both sides: y + 18 = 3x; divide both by 3: x = y + 183.
Example 2
Which is the formula S = 6(m − t) with t as its subject?
- A. t = S6 − m
- B. t = m − S6
- C. t = m − S6
- D. t = m − 6S
Choose the right answer
Show the answer and working
Answer: B. t = m − S6
Divide both sides by 6: S6 = m − t; then move the terms: t = m − S6.
Example 3
Make x the subject of y = 20 − 5x: x = − y
Fill in each blank
Show the answer and working
Answer: 20, 5
Move 5x to the left and y to the right: 5x = 20 − y; divide by 5: x = 20 − y5.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Which is the formula P = 5n + 4 with n as its subject?
- A. n = P5 − 4
- B. n = 5(P − 4)
- C. n = P − 45
- D. n = P + 45
Choose the right answer
Answer:
2.From P = 3(l + w), it follows that l = P4 − w.
True or false?
Answer:
3.Which is the formula y = x + 166 with x as its subject?
- A. x = 6y − 16
- B. x = 6(y − 16)
- C. x = 6y + 16
- D. x = y6 − 16
Choose the right answer
Answer:
4.Which is the formula S = 9(m − t) with t as its subject?
- A. t = m − S9
- B. t = m − S9
- C. t = S9 − m
- D. t = m − 9S
Choose the right answer
Answer:
5.Make x the subject of y = 28 − 2x: x = − y
Fill in each blank
Answer:

All the answers

1. C. n = P − 45
2. False
3. A. x = 6y − 16
4. A. t = m − S9
5. 28, 2

Free worksheet: Changing the subject of a formulaWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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