Four Operations with Integers
The four operations, addition, subtraction, multiplication and division, are calculated on large whole numbers using formal written methods: column addition and subtraction, including exchanging, sometimes called borrowing, and short and long multiplication and division, including deciding what to do with a remainder. These written methods allow accurate calculation with numbers too large to work out mentally or without a calculator, and underpin almost every other topic in maths.
Before you start
No specific prerequisites - this is a good place to start.
Method
- For column addition, line up the digits by place value (units under units, tens under tens, and so on), add each column starting from the units, and carry any ten into the next column left.
- For column subtraction, line up the digits by place value and subtract starting from the units column, exchanging 1 from the column to the left whenever the top digit is smaller than the digit below it.
- For short multiplication (multiplying by a single digit), multiply each digit of the larger number by the single digit starting from the units, carrying and adding as you go.
- For long multiplication (multiplying two multi-digit numbers), multiply the first number by each digit of the second number separately, shifting each row left according to place value, then add the rows together.
- For short division, divide into the number from the left, carrying any remainder into the next digit.
- For long division with a multi-digit divisor, estimate how many times the divisor fits into each part of the number, subtract the multiple, bring down the next digit, and repeat.
- Decide what to do with a remainder based on the context: leave it as 'remainder r', convert it to a fraction or decimal, or round the answer up or down to a sensible whole number.
Worked example
A school is organising a trip for 314 pupils. Each coach seats 48 pupils. Work out how many coaches are needed so that every pupil has a seat.
- Divide 314 by 48: 48 x 6 = 288, and 314 - 288 = 26, so 314 / 48 = 6 remainder 26.
- This means 6 full coaches carry 288 pupils, leaving 26 pupils without a seat.
- Since every pupil needs a seat, a 7th coach is needed for the remaining 26 pupils, even though it will not be full.
- Round the division answer UP to the next whole number rather than down (or ignoring the remainder): 7 coaches are needed.
- Check: 7 coaches x 48 seats = 336 seats, which is enough for the 314 pupils, with 22 seats spare.
Practice questions
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Q1A warehouse receives deliveries of 4268 tins in the morning and 3754 tins in the afternoon. Work out the total number of tins delivered that day.Show answer
Answer: 8022 tins
Q2A stadium has a capacity of 32500 seats. If 27846 tickets have been sold, work out how many seats remain unsold.Show answer
Answer: 4654 seats
Q3A minibus company owns 8 minibuses, each with 29 seats. Work out the total number of seats across all the minibuses.Show answer
Answer: 232 seats
Q4A printing press produces 236 leaflets per box. Work out how many leaflets are in 47 boxes.Show answer
Answer: 11092 leaflets
Q51752 pencils are shared equally between 6 classes. Work out how many pencils each class receives.Show answer
Answer: 292 pencils
Q6A ribbon of length 275 cm is cut into pieces, each 12 cm long. Work out how many complete pieces can be cut, and how much ribbon is left over.Show answer
Answer: 22 complete pieces, with 11 cm left over (12 x 22 = 264, 275 - 264 = 11)
Q7A theatre has 24 rows of seats with 18 seats in each row. On a sold-out night, 9 seats were left empty due to no-shows. Work out how many seats were actually occupied.Show answer
Answer: 423 seats (24 x 18 = 432, then 432 - 9 = 423)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A factory packs 1000 chocolate bars into boxes of 24. (a) Work out how many complete boxes can be filled. (b) Work out how many chocolate bars are left over after filling the complete boxes.
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A charity is packing 1428 emergency food parcels. Each delivery van can carry 85 parcels, and the charity has 15 vans. (a) Work out the total number of parcels the 15 vans can carry in one trip. (b) Determine whether one trip by all 15 vans is enough to deliver all 1428 parcels, showing your working.
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Without a calculator, work out 384 x 26. Show your full method.
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Free printable worksheet
Want more practice on paper? Download the four operations with integers worksheet pack - 5 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 5 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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