What Is Long Division? A Step-By-Step Guide For Primary School
Long division is usually used to divide three or four-digit numbers by two or more digit numbers. Children must understand the concept of division before teaching them long division in Year 6. This formal method is quite an abstract process.
3 Long Division Worksheets for Year 3-6 Classes
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Download Free Now!What is long division?
Long division is a formal method of division often called the bus stop method. See the examples below from the Mathematics Appendix 1 in the national curriculum.
The first two examples above are commonly known as ‘chunking’. The third example is an expanded version of the short division method.
Long division differs from the short division method as it is less compact. The long method of division is used most often when dividing by large numbers. In the primary curriculum this is usually a 2-digit number (or three digits as a challenge). You can use it with or without remainders.
See also: What is division
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Watch Skye in actionHow to do long division step-by-step
Long division is laid out in the same way as short division:
- Dividend (the number being divided) under the ‘bus stop’,
- Divisor (number the dividend is being divided by) to the left of the ‘bus stop’;
- Quotient (answer) on top, with each place value aligned with the dividend.
Chunking
The example below uses the ‘chunking’ form of long division to calculate 432 ÷ 15.
This variation of the long division method involves ‘chunking’ a section of the dividend a bit at a time.
- Firstly, by subtracting 20 lots of the divisor, which leaves 132;
- Then, subtracting another 8 lots of the divisor, which leaves 12.
As this amount is smaller than the divisor, this is the remainder. The quotient is 28, so the final answer is 28r12 (or, if represented as a fraction, 28 and \frac{12}{15} or 28 and \frac{4}{5} when simplified).
Long division steps
There are five long division steps to simplify this version of the method:
- Divide
- Multiply
- Subtract
- Bring the next number down
- Repeat
Here’s how to apply these steps:
1. Divide
- Start with the first digit of the dividend. In this case, divide 4 hundreds by 15.
- We cannot divide 4 by 15 so, we could place a 0 above the 4 here. Or, we can view the 4 hundreds as 40 tens alongside the 3 tens (the next digit of the dividend).
- Now we can divide 43 tens by 15, which is 2 tens.
- This digit is placed above the 3 tens and becomes the first digit of the quotient.
2. Multiply
We need to calculate the remainder for this first step of the division. to do this:
- Multiply the first digit of the quotient, 2 tens, by the divisor, 15, to get 30 tens 2 x 15 = 30
- Place this underneath the dividend, making sure to align the place values correctly.
3. Subtract
Now we must finish calculating the remainder for this first step of the division:
- Subtract 30 tens from 43 tens to get 13 tens – 43 – 30 = 13
4. Bring the next digit down
In short division, we would place the remainder from each step before the next digit in the dividend. In this case, we would write 13 on the top left of the digit ‘2’ to read 132.
In long division, we bring the next digit of the quotient down. This achieves the same thing and is easier to read!
5. Repeat:
Now we start the division process again from…
- Divide: Divide 132 ones by 15 and place the answer, in the quotient. 132 ÷ 15 = 8;
- Multiply: Multiply the next digit of the quotient, 8 ones, by the divisor, 15, and place the answer underneath 132 ones. 8 x 15 = 120;
- Subtract: Finish calculating the remainder by subtracting 120 ones from 132 ones. 130 – 120 = 12;
- Bring the next digit down: As the quotient isn’t a whole number we need to add a decimal point and a zero to calculate the remainder as a decimal. The zero comes down to make 120 tenths;
- Repeat: Divide 120 tenths by 15 to get 8 tenths and place this in the quotient as the first – and only – decimal place. 120 ÷ 15 = 8 ;
Multiply 8 tenths by 15 to get 120 tenths. 8 x 15 = 120;
Subtract this from 120 tenths to calculate the remainder, 120 – 120 = 0;
There is now no next digit to bring down as the remainder is now 0;
The calculation is complete.
As you can see from the example below, you can use short division to solve this calculation. Both methods give the correct answers as the ‘long’ method is just the expanded version of the ‘short’ method.
Rather than doing some mentally calculating the remainder for each step in the short division method, long division lays these same calculations out as part of the method itself.
How to explain long division
If children struggle with multiplication and division, particularly times tables, it helps to list multiples of the divisor before completing the division. This reduces the cognitive demand on the child when working through the method.
Here’s an example:
First, list 9 multiples of the divisor. This can be calculated using:
- Repeated addition – 15 + 15 = 30, + 15 = 45, + 15 = 60, etc.; or
- Partitioning – partition 15 into 10 and 5; list the multiples of 10 – 10, 20, 30 etc. – and the multiples of 5 – 5, 10, 15 etc. and then add them together to create each multiple – 10 + 5 = 15, 20 + 10 = 30, 30 + 15 = 45 and so on.
When completing step 1 of this method, the multiples make it a lot easier.
In the example above, when calculating 43 tens divided by 15, we can see that 43 is larger than 30 but less than 15 ones larger. Therefore, we must write 2 in the quotient because only 2 lots of 15 ones fit into 43.
We can continue the division process until we get to the ‘repeat’ step and calculate 132 ones divided by 15. It’s clear to see that 8 multiples of 15, which is 120 is the largest multiple of 15 to fit into 132.
Although pupils usually use short division when dividing by one digit, encourage pupils to try long division with one digit to start with. However, when teaching the long division method, comparing both (as in the example below) is a clear sequential step to bridge short and long methods.
Worked examples
Having a bank of long division examples and long division questions is key for any Year 6 teacher. You can use the following worked examples and practice problems as a starting point for teaching long division.
- 45,041 ÷ 73
Answer: 617
2. Adam is making booklets. Each booklet must have 34 sheets of paper. He has 2 packets of paper. There are 500 sheets of paper in each packet. How many complete booklets can Adam make from 2 packets of paper?
Answer: 2 packets of 500 sheets = 1,000 sheets. 1,000 ÷ 34 = 29 complete booklets
3. A supermarket manager needs to order 1,176 apples. Apples are sold in trays containing 28 apples. How many trays of apples does the manager need to order?
Answer: 1,176 ÷ 28 = 42 trays
Practice problems
- 1,632 ÷ 24 =
Answer: 68 - 42,028 ÷ 79 =
Answer: 532 - For a school trip, each coach holds 42 passengers. If there are 521 children and teachers in total, how many coaches does the school need to book?
Answer: 13 coaches - A factory makes 4,923 toy cars and packs them in boxes of 15. How many toy cars are left over?
Answer: 3 - 21 people each win an equal share of £9,072. How much does each person win?
Answer: £432
When do children learn about long division in school?
Long division is taught in the final year of primary school. The National Curriculum states that Year 6 pupils must learn to divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.
Third Space Learning supports pupils who need extra help with long division through one-to-one online maths tutoring. Sessions are personalised to the needs of each pupil to close learning gaps and boost confidence in maths.
How does long division relate to other areas of maths?
Sometimes, pupils must use long division in multi-step problems–word problems requiring more than one mathematical operation to solve it, e.g. addition and multiplication. As the cognitive demand of a maths problem like this is already quite high, short division is a more appropriate method.
How does long division link to real life?
Any long division scenario can relate to a real-life example. When sharing something equally between a large number of groups, use long division.
For example, Arthur has 1,459 sweets to share between the 29 pupils in his class, how many sweets do they each get?
FAQs
Divide, multiply, subtract, bring the next digit down and repeat the previous steps.
Long division is the expanded version of short division – each step is exactly the same but we just write it out instead of doing it mentally!
Long division is more accurate than short division when dividing by larger numbers because there is less we have to ‘hold’ in our head. All the calculations are laid out for us.
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