IGCSE Math RevisionExample 1
Work out \(347 \times 26\).
- \(347 \times 20 = 6940\)
- \(347 \times 6 = 2082\)
- \(6940 + 2082 = 9022\)
Answer: \(9022\)
Cambridge IGCSE Maths (0580) · Non-calculator · 1.6
Long multiplication and division without a calculator
Without a calculator, every multi-step question still needs a product or a quotient worked out by hand. A reliable written method, set out neatly, earns the method marks even if one digit slips.
- Core and Extended
- Paper 1 (Core) and Paper 2 (Extended)
- 8 questions
- Free, no sign-in
The method
- Multiplying: split the smaller number into tens and units (a grid works too), multiply each part, then add the rows.
- Decimals: multiply as whole numbers, then put back as many decimal places as the two numbers had between them.
- Dividing: use short division (the bus stop) for one-digit divisors; for two-digit divisors, write out the first few multiples of the divisor before you start.
- Dividing by a decimal: multiply both numbers by the same power of 10 until the divisor is a whole number, then divide.
- Order of operations: brackets, then indices, then division and multiplication from left to right, then addition and subtraction.
- Check the size: a quick estimate tells you if the decimal point is in the right place.
Worked examples
Example 2
Work out \(1.56 \div 0.12\).
- Multiply both numbers by \(100\): \(1.56 \div 0.12 = 156 \div 12\).
- \(12 \times 13 = 156\), so \(156 \div 12 = 13\).
Answer: \(13\)
Common slips
- Forgetting the zero placeholder when multiplying by the tens digit.
- Counting decimal places in the answer instead of in the two numbers being multiplied.
- Moving the decimal point in only one of the numbers when dividing by a decimal.
- Working left to right through + and × instead of doing × and ÷ first.
Practice questions
No calculator. Write down every step, then open the worked answer.
Question 1
Work out \(238 \times 47\).
Show the worked answer
- \(238 \times 40 = 9520\)
- \(238 \times 7 = 1666\)
- \(9520 + 1666 = 11186\)
Answer: \(11186\)
Question 2
Work out \(912 \div 16\).
Show the worked answer
- Multiples of \(16\): \(16 \times 5 = 80\), \(16 \times 7 = 112\).
- \(91 \div 16 = 5\) remainder \(11\); bring down the \(2\) to make \(112\).
- \(112 \div 16 = 7\).
Answer: \(57\)
Question 3
Work out \(4.7 \times 0.36\).
Show the worked answer
- \(47 \times 36 = 47 \times 30 + 47 \times 6 = 1410 + 282 = 1692\)
- The two numbers have \(1 + 2 = 3\) decimal places between them, so the answer has \(3\).
Answer: \(1.692\)
Question 4
Work out \(8.64 \div 0.24\).
Show the worked answer
- Multiply both numbers by \(100\): \(864 \div 24\).
- \(24 \times 30 = 720\), and \(864 - 720 = 144 = 24 \times 6\).
Answer: \(36\)
Question 5
Work out \(6 + 18 \div 3 \times 2 - 4\).
Show the worked answer
- Division and multiplication first, left to right: \(18 \div 3 = 6\), then \(6 \times 2 = 12\).
- \(6 + 12 - 4 = 14\)
Answer: \(14\)
Question 6
Work out \(7.2 \div 0.009\).
Show the worked answer
- Multiply both numbers by \(1000\): \(7200 \div 9\).
- \(7200 \div 9 = 800\)
Answer: \(800\)
Question 7
A school is taking \(1240\) students on a trip. Each coach has \(53\) seats.
Work out the smallest number of coaches needed.
Show the worked answer
- \(53 \times 20 = 1060\) and \(1240 - 1060 = 180\).
- \(53 \times 3 = 159\), so \(23\) coaches seat \(1219\) students, which is not enough.
- \(53 \times 24 = 1272\), which is enough.
Answer: \(24\) coaches
Question 8
A theatre ticket costs $18.75. Work out the cost of \(36\) tickets.
Show the worked answer
- \(18.75 \times 36 = 18.75 \times 4 \times 9 = 75 \times 9\)
- \(75 \times 9 = 675\)
Answer: $675
Every example and question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. The syllabus is summarised in our own words: check the official 0580 syllabus.
Keep going
- The Four Operations questions for 0580: Core and Extended, each labelled calculator or non-calculator
- Number practice for 0580, then My mistakes and a Skill Builder on what you missed
- The four operations notes and the 0580 formula sheet
- 0580 past papers: time yourself on a specimen Paper 1 or Paper 2
- All six non-calculator methods
Questions students ask
Which 0580 papers test long multiplication and division without a calculator?
Long multiplication and division is on both tiers (syllabus 1.6), so it can come up on Paper 1 (Core) and Paper 2 (Extended), the two non-calculator papers, as well as on the calculator papers.
Are these Cambridge questions?
No. The method is explained in our own words, and every example and question was written for IGCSE Math Revision and checked independently before publishing. For real papers, use the Cambridge copies linked from our 0580 past papers page.