A multi-step problem is one that cannot be solved with just one calculation. You need to work through several steps, and the answer from one step feeds into the next.
What Makes a Problem Multi-Step?
Multiple operations: The problem involves addition, subtraction, multiplication, or division in sequence.
Hidden information: Some values need to be calculated before you can find the final answer.
Context clues: Words like "then," "after," "first," "next," or "finally" often signal multiple steps.
Real-world scenario: The problem describes a situation that naturally involves several actions.
How to Identify the Steps
When you read a multi-step problem, look for the question at the end. Then, work backwards: what do I need to know to answer this? What do I need to find first?
Example: Identifying Steps
Problem: "A shop buys t-shirts for £4.50 each. They mark them up by 50%. How much profit do they make on 12 t-shirts?"
What do I need to find? Total profit on 12 shirts.
Step 1: Calculate the markup per shirt (50% of £4.50)
Step 2: Multiply the profit per shirt by 12
Worked Example 1: A Shopping Scenario
You have £50. You buy 3 notebooks at £2.99 each. Then you buy a pen for £1.25. How much change do you get?
STEP 1:
Calculate the cost of 3 notebooks: 3 × £2.99 = £8.97
STEP 2:
Add the cost of the pen: £8.97 + £1.25 = £10.22
STEP 3:
Subtract from your starting amount: £50 − £10.22 = £39.78
Your change is £39.78
Worked Example 2: A Travel Scenario
You cycle at 15 km/h for 2.5 hours, then walk at 4 km/h for 1 hour. What is the total distance you cover?
STEP 1:
Distance cycled: 15 × 2.5 = 37.5 km
STEP 2:
Distance walked: 4 × 1 = 4 km
STEP 3:
Total distance: 37.5 + 4 = 41.5 km
Total distance = 41.5 km
✓ Quick Check 1 — Identifying Multi-Step Problems
Question 1 of 10
Planning Your Approach
The key to solving multi-step problems successfully is to plan before you calculate. Take time to understand the problem, then decide what operations you need.
Breaking Down Complex Problems
Underline key information: Numbers, percentages, units, and relationships.
Circle the question: What are you asked to find?
List what you know and what you need: Create a "given" and "find" section.
Decide the order: What calculation comes first? What depends on the previous answer?
Tip: Write down each step as a mini-equation or calculation. Don't try to do everything in your head — it's easy to make mistakes.
Order of Operations (BODMAS/PEMDAS)
When you have multiple operations in a multi-step problem, remember the order:
Brackets/Parentheses
Orders (exponents, square roots)
Division and Multiplication (left to right)
Addition and Subtraction (left to right)
Worked Example 3: A Budgeting Scenario
You earn £12 per hour and work 25 hours per week. Your rent is 40% of your weekly earnings. How much do you have left after paying rent?
STEP 1:
Calculate weekly earnings: £12 × 25 = £300
STEP 2:
Calculate rent (40% of £300): £300 × 0.4 = £120
STEP 3:
Subtract rent from earnings: £300 − £120 = £180
You have £180 left after paying rent.
Worked Example 4: A Construction Problem
A rectangular garden is 8 metres long and 5 metres wide. You need to fence three sides (not the back). Fencing costs £15 per metre. What is the total cost?
STEP 1:
Identify which sides: 2 lengths of 8 m + 1 width of 5 m
STEP 2:
Calculate total metres of fencing: (8 + 8 + 5) = 21 metres
STEP 3:
Multiply by cost per metre: 21 × £15 = £315
The total cost is £315.
Worked Example 5: Applying BODMAS to a Multi-Step Problem
Sometimes a multi-step problem can be written as one expression with several operations mixed together. Getting the order right matters — done in the wrong order, you get a completely different (wrong) answer.
A café sells 3 coffees at £2.80 each and 2 cakes at £3.50 each, then takes £1.60 off the total with a loyalty discount. As one expression: 3 × £2.80 + 2 × £3.50 − £1.60. What is the total?
STEP 1:
BODMAS says multiplication comes before addition/subtraction, so do both multiplications first: 3 × £2.80 = £8.40, and 2 × £3.50 = £7.00
STEP 2:
Now the expression is £8.40 + £7.00 − £1.60. Work left to right: £8.40 + £7.00 = £15.40
STEP 3:
Then subtract the discount: £15.40 − £1.60 = £13.80
Total = £13.80
Why order matters here: if you worked strictly left to right instead — (3 × £2.80) then + 2 = 10.4, ×£3.50 = £36.40, − £1.60 = £34.80 — you would get a completely wrong total. BODMAS tells you the two multiplications must be done before any adding or subtracting, no matter what order they appear in the sentence.
Worked Example 6: A Longer Multi-Step Problem
A youth club is organising a trip. Coach hire costs £180, split equally among the 24 people going. Each person also pays £8.50 for entry to the venue. On the day, 3 people cancel and get a full refund of their coach share and entry fee. How much money does the club actually collect in total?
STEP 1:
Coach cost per person: £180 ÷ 24 = £7.50
STEP 2:
Total each person pays (coach share + entry): £7.50 + £8.50 = £16.00
STEP 3:
Number of people who actually go: 24 − 3 = 21
STEP 4:
Total collected from those 21 people: 21 × £16.00 = £336.00
The club collects £336.00 in total. Notice how the answer from each step becomes an input to the next — this is what makes it a genuine multi-step problem, not just a sequence of unrelated sums.
✓ Quick Check 2 — Multi-Step Problem Solving
Question 1 of 10
Checking Your Work
Multi-step problems are where mistakes are most common. By checking as you go, you catch errors early and build confidence in your answer.
Verification Steps
Check each calculation: Use a calculator or work through it again. Does the maths make sense?
Sense-check the answer: Is your answer reasonable? If you earn £300/week, your rent can't be £3,000.
Check units: Do your units match? (e.g., metres, kilograms, pounds sterling)
Re-read the question: Have you answered what was actually asked?
Work backwards (if possible): Start with your answer and reverse the operations to see if you get back to the original information.
Common Mistakes to Avoid
Forgetting a step: Re-read the problem carefully. Check you have used all the given information.
Wrong order of operations: If multiplying and adding, multiply first (unless brackets say otherwise).
Mixing up percentages: 40% markup means final price = original + 40% of original (not just 40% of original).
Unit confusion: Is the answer in pounds or pence? Metres or centimetres? Check your units throughout.
Arithmetic errors: Especially with decimals. Always double-check key calculations.
Worked Example 5: Checking Your Answer
A shop buys tablets for £150. They mark them up by 30% for sale. A customer buys one and gets 10% discount. What do they pay?
Does this make sense? Cost was £150. With 30% markup it went to £195. A 10% discount brings it to £175.50 — still above cost. ✓
The customer pays £175.50.
✓ Quick Check 3 — Checking and Verifying
Question 1 of 10
Practice: Solve These Multi-Step Problems
Solve each problem step-by-step. Write out your working, then enter your final answer below.
Problem 1: Shopping with Discount
You buy 4 books at £8.99 each. The shop offers 15% discount. How much do you pay in total?
Problem 2: Travel and Time
You drive at 60 mph for 2 hours, then at 50 mph for 1.5 hours. What is the total distance?
Problem 3: Budgeting
Your monthly salary is £2,500. Rent is 30%, food is £400, transport is £200. How much is left for savings and other costs?
Problem 4: Shopping with Discount
You buy 3 shirts at £15.50 each. The shop offers 10% discount. How much do you pay in total?
Problem 5: Travel and Time
You drive at 40 mph for 3 hours, then at 70 mph for 1 hour. What is the total distance?
Problem 6: Budgeting
Your monthly salary is £1,800. Rent is 25%, food is £250, travel is £120. How much is left for savings and other costs?
Problem 7: Shopping with Discount
You buy 5 pens at £2.20 each. The shop offers 20% discount. How much do you pay in total?
Problem 8: Travel and Time
You cycle at 15 mph for 2 hours, then walk at 4 mph for 0.5 hours. What is the total distance?
Problem 9: Budgeting
Your monthly salary is £3,200. Rent is 35%, food is £500, bills are £300. How much is left for savings and other costs?
Problem 10: Shopping with Discount
You buy 6 notebooks at £1.75 each. The shop offers 5% discount. How much do you pay in total?
⚠ Things to Watch Out For
Not checking the final answer makes sense: Always sense-check your answer against the context — a weekly rent of £3,000 on a £300 salary should raise a red flag.
Skipping a step: Re-read multi-step problems carefully and check you have used every piece of given information before finishing.
Wrong order for percentage changes: A markup then a discount are applied to DIFFERENT amounts in sequence — the discount is a percentage of the marked-up price, not the original price.
Units not matching throughout: Check every measurement is in the same unit (pounds vs pence, metres vs centimetres) before combining them.
Rounding too early: Carry full precision through each step of a multi-step calculation and round only the final answer.