Worded Problems Set F
Multi-step worded problems combine two or more operations (addition, subtraction, multiplication and division) inside a single question, usually set in a real-life context such as shopping, sharing out amounts, or planning a journey. The skill being tested is not the arithmetic itself but working out, from the words alone and without being told which operation to use, what calculation is needed at each stage and in what order.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole problem once, all the way through, before doing any calculating, so you understand the overall situation.
- Underline or note every number given in the question, along with the unit it belongs to (pounds, minutes, items, and so on).
- Decide exactly what the question is asking for at the end, and work backwards from that to see which quantities you need to combine to get there.
- Break the problem into separate smaller calculations, writing down and labelling the answer to each stage clearly before starting the next.
- Watch out for hidden intermediate steps, such as needing to find a total or a difference first before you can use it in a later part of the calculation.
- Check your final answer is reasonable for the context: a money answer should not be negative, and a number of people or objects should be a whole number.
Worked example
A school orders 15 boxes of pencils, each box containing 24 pencils. The pencils are then shared equally between 7 classes, with any leftover pencils kept in the office. How many pencils does each class receive, and how many are left over?
- Find the total number of pencils ordered: 15 x 24.
- 15 x 24 = 360 pencils in total.
- Divide the total between 7 classes: 360 / 7 = 51 remainder 3, since 7 x 51 = 357.
- Each class receives 51 pencils, and 3 pencils are left over.
- Check: 7 x 51 = 357, and 357 + 3 = 360, which matches the total number of pencils ordered.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A bakery makes 18 trays of 12 muffins each. How many muffins does it make in total?Show answer
Answer: 216 (18 x 12)
Q2A shop sells pens in packs of 8 for 3.20 pounds per pack. What is the cost of one pen?Show answer
Answer: 0.40 pounds (3.20 / 8)
Q3Maya buys 3 books at 4.50 pounds each and pays with a 20 pound note. How much change does she receive?Show answer
Answer: 6.50 pounds (20 - (3 x 4.50) = 20 - 13.50)
Q4A minibus can carry 14 passengers. How many minibuses are needed to transport 100 people?Show answer
Answer: 8 (100 / 14 = 7 remainder 2, and the 2 remaining people still need a minibus, so round up from 7 to 8)
Q5A recipe for 4 people needs 300 g of rice. How much rice is needed for 10 people?Show answer
Answer: 750 g (300 / 4 = 75 g per person, then 75 x 10)
Q6A charity raises 840 pounds, shared equally between 5 projects. How much does each project receive?Show answer
Answer: 168 pounds (840 / 5)
Q7A factory produces 2,400 toys in 8 hours. How many toys does it produce per hour?Show answer
Answer: 300 (2,400 / 8)
Q8Ben has 45 pounds. He buys 3 games at 12 pounds each. How much money does he have left?Show answer
Answer: 9 pounds (45 - (3 x 12) = 45 - 36)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A school is organising a trip for 168 pupils. Each coach holds 45 pupils, and coaches cost 180 pounds each to hire. (a) How many coaches are needed? (b) What is the total cost of hiring the coaches?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A market stall buys 240 apples at 15 pence each. The stall sells all the apples in bags of 6, at 1.20 pounds per bag. (a) What is the total cost of buying the apples, in pounds? (b) How many bags of apples can be made? (c) What is the total profit made from selling all the bags?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the worded problems set f worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 25 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on worded problems set f, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.