Worded Problems Set B
Worded Problems Set B is the second set of worded problems, moving beyond single, familiar contexts into comparison, 'how many more or fewer', problems, and into questions with a remainder or a leftover amount that must be interpreted sensibly, such as deciding whether to round a number of coaches or boxes up or down. It builds on Worded Problems Set A by testing the trickier judgement calls that worded problems often hide.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a comparison problem asking 'how many more or fewer', find the difference between the two quantities using subtraction, not addition.
- For a 'how many are needed' problem involving groups, such as coaches or boxes, divide the total by the group size, and if there is a remainder, round the number of groups UP so that everyone or everything fits.
- For a problem asking how many complete groups you can make, divide the total by the group size and round the number of groups DOWN, ignoring any leftover.
- Decide which rounding rule applies before calculating, by asking what happens to anyone or anything left over in the real-life situation.
- Show the division and the remainder clearly, then state explicitly whether you rounded up or down and why.
- Reread the question to check whether it wants the number of groups, the number left over, or both.
Worked example
A school is taking 172 pupils on a trip. Each coach holds 40 pupils. How many coaches are needed so that every pupil has a seat?
- Divide the total pupils by the coach capacity: 172 / 40.
- 40 x 4 = 160, which leaves 172 - 160 = 12 pupils without a seat.
- Since these 12 pupils still need a coach, round the number of coaches up from 4 to 5.
- 5 coaches are needed.
Practice questions
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Q1A shop has 53 apples and 38 oranges. How many more apples than oranges does it have?Show answer
Answer: 15 more apples
Q2A minibus seats 16 passengers. 90 people need transport. How many minibuses are needed for everyone to have a seat?Show answer
Answer: 6 minibuses
Q3A florist has 100 stems and makes bunches of 7 stems each, selling only complete bunches. How many complete bunches can she make?Show answer
Answer: 14 bunches
Q4Ravi has 245 stickers. His sister has 178. How many more stickers does Ravi have?Show answer
Answer: 67 more stickers
Q5A carton holds 6 eggs. A farmer has 100 eggs. How many complete cartons can be filled, and how many eggs are left over?Show answer
Answer: 16 cartons, with 4 eggs left over
Q6Team A scored 87 points. Team B scored 59 points. By how many points did Team A win?Show answer
Answer: 28 points
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A library has 250 books to pack into crates. Each crate holds 24 books. How many crates does the library need to pack every book, and how many books are in the last, not-full crate?
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In a maths test out of 100 marks, Priya scored 68 marks and Sam scored 45 marks. How many more marks than Sam did Priya score, and what percentage of the total marks is this difference?
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Free printable worksheet
Want more practice on paper? Download the worded problems set b worksheet pack - 10 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 4 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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