Multiplication and Division: Formal Written Methods
In Year 5, pupils use formal written methods to multiply and divide with larger numbers. They use short multiplication to multiply a number with up to 4 digits by a single digit, and long multiplication to multiply a number with up to 4 digits by a two-digit number, setting out the working in columns.
Before you start
Make sure you're comfortable with these topics first:
Method
- For short multiplication, write the larger number above the smaller (single-digit) number, line up the place-value columns, then multiply each digit of the larger number by the single digit, starting from the ones column and carrying into the next column.
- For long multiplication, split the two-digit multiplier into tens and ones, multiply the larger number by the ones digit first, then by the tens digit (writing a placeholder zero in the ones column of this second row), and add the two results together.
- For short division (the bus stop method), divide the digits of the number one at a time from the left, carrying any remainder into the next digit as tens of that digit.
- If the first digit of the number being divided is smaller than the divisor, divide the first two digits together instead, and carry any remainder as normal from there.
- At the end of a short division, decide what to do with any final remainder: give it as 'r' plus a number, convert it to a fraction of the divisor, or round the answer up or down, depending on what the question is asking.
- Estimate the answer to a multiplication or division before calculating, by rounding the numbers involved, so you can check your formal method has not gone wrong.
- Check a multiplication by dividing the answer by one of the original numbers, and check a division by multiplying the answer (ignoring any remainder) by the divisor and adding the remainder back.
Worked example
A coach company has 236 coaches. Each coach can carry 47 passengers. Use long multiplication to find the total number of passengers all the coaches can carry.
- Split 47 into 40 and 7.
- Multiply 236 by 7 (the ones digit): 236 x 7 = 1,652.
- Multiply 236 by 40 (the tens digit), writing a zero in the ones column first: 236 x 4 = 944, so 236 x 40 = 9,440.
- Add the two results together: 1,652 + 9,440 = 11,092.
- So the coaches can carry 11,092 passengers in total.
Practice questions
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Q1Use short multiplication to work out 3,428 x 6.Show answer
Answer: 20,568
Q2Use short division to work out 936 divided by 4, using the bus stop method.Show answer
Answer: 234 (936 / 4 = 234)
Q3Use long multiplication to work out 154 x 23.Show answer
Answer: 3,542
Q4Divide 2,675 by 5 using short division. Is there a remainder?Show answer
Answer: 535, with no remainder (5 x 535 = 2,675)
Q5Divide 619 by 7 using short division. Give your answer with a remainder.Show answer
Answer: 88 remainder 3 (7 x 88 = 616, and 619 - 616 = 3)
Q6A minibus company needs to seat 350 pupils on minibuses that each hold 16 pupils. Use short division to find how many minibuses are needed, remembering to round up if there is a remainder.Show answer
Answer: 22 minibuses (350 / 16 = 21 remainder 14, so 22 minibuses are needed to seat everyone, since 21 would leave 14 pupils without a seat)
Q7Use long multiplication to work out 68 x 34.Show answer
Answer: 2,312
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A factory packs biscuits into boxes of 8. It has 3,254 biscuits to pack. (a) Use short division to work out how many full boxes of 8 biscuits can be packed. (2 marks) (b) How many biscuits will be left over? (1 mark)
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A school orders 27 identical boxes of exercise books. Each box contains 145 books. (a) Use long multiplication to find the total number of exercise books ordered. (3 marks) (b) The books need to be shared equally between 9 classrooms. How many books does each classroom receive? (2 marks)
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Use short multiplication to work out 2,809 x 5.
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Free printable worksheet
Want more practice on paper? Download the multiplication and division: formal written methods 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.
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