Long Division – The Bus Stop Method

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Long Division

There are different methods that can be used for long division but the most commonly used in the UK is the Bus Stop method.

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Bus Stop Method

This method for long division is called the Bus Stop method, since it looks like a bus stop. This method allows us to divide numbers to find integer answers or answers that have a remainder. There are a few steps that you need to follow.

Example: Calculate 288÷9288 div 9.

Step 1: We start by putting the division into the Bus Stop form as show below.

Bus Stop Method - Long division

Step 2: We see how many times 99 goes into 22, the first digit. The answer is 0textcolor{blue}{0} so the 2textcolor{red}{2} is carried onto the next digit to make a new number, 2828.  The zero goes at the top.

Bus Stop Method - Long division

Step 3: Now, we see how many times 99 goes into 2828. We know that 3×9=273 times 9=27, so 99 goes into 2828 3textcolor{blue}{3} times with a remainder 1textcolor{red}{1}, which is then carried in front of the next digit to make a new number, 1818. The three goes at the top.

Step 4: Then, we see how many times the 99 goes into 1818, which is 2textcolor{blue}{2}. The two then goes at the top. These two steps are combined in the image below.

Bus Stop Method - Long division

So,

288÷9=32288 div 9 = textcolor{limegreen}{32}

Note: If 99 did not go into the number in the last step, for example if the question asked to calculate 289÷9289 div 9, then 99 goes into 1919 2textcolor{blue}{2} times, with a remainder 1textcolor{red}{1}. So we would say that the answer had a remainder of 11 and we would write

289÷9=32 r 1289 div 9 = textcolor{limegreen}{32} text{ r } textcolor{red}{1}

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Example: Long Division with a Remainder

Calculate 67÷567 div 5

[2 marks]

We use the same bus stop method as shown before, but this time we have a remainder.

Bus Stop Remainder

67÷5=13 r 267 div 5 = textcolor{limegreen}{13} text{ r } textcolor{red}{2}

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Long Division – The Bus Stop Method Example Questions

Question 1: Work out 315÷14315 div 14.

[2 marks]

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Here we’re going to use the bus stop method.

1414 goes into 33 zero times, so we write a zero above the line and a small 33 – the remainder – in between the 33 and the 11. Then, we see how many times 1414 goes into 3131, writing the result above the line and the remainder just before the next digit of the dividend.

Repeat this process until you get the complete answer, which looks like,

 

          0  2  2  .  514)33135.70;;;;;0;2;2;.;5\14overline{left)3{}^31{}^35.{}^70right.}

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Question 2: Calculate 225÷15225 div 15.

[2 marks]

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Here we’re going to use the bus stop method,

1515 goes into 22 zero times, so we write a zero above the line and a small 22 – the remainder – in between the 22 and the 22. Then, we see how many times 1515 goes into 2222, which is 11,  writing the result above the line and the remainder, 77,  just before the next digit of the dividend.

Repeat this process until you get the complete answer, which looks like,

 

          0  1  515)22275;;;;;0;1;5\15overline{left)2{}^22{}^75right.}

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Question 3: Calculate 4320÷1604320 div 160.

[2 marks]

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Here we’re going to use the bus stop method,

160160 goes into 44 zero times, so we write a zero above the line and a small 44 – the remainder – in between the 44 and the 33. Then, we see how many times 160160 goes into 4343, which is also zero,  writing the result above the line and the remainder, 4343,  just before the next digit of the dividend.

Repeat this process until you get the complete answer, which looks like,

 

              0    0    2    7160)4434321120;;;;;;;0;;0;;2;;7\160overline{left)4{}^43{}^{43}2{}^{112}0right.}

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Question 4: Calculate 299÷13299 div 13.

[2 marks]

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Here we’re going to use the bus stop method,

1313 goes into 22 zero times, so we write a zero above the line and a small 22 – the remainder – in between the 22 and the 99. Then, we see how many times 1313 goes into 2929, which is 22,  writing the result above the line and the remainder, 33,  just before the next digit of the dividend.

Repeat this process until you get the complete answer, which looks like,

 

        0  2  313)22939;;;;0;2;3\13overline{left)2{}^29{}^39right.}

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Question 5: Calculate 234÷9234 div 9.

[2 marks]

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Here we’re going to use the bus stop method,

99 goes into 22 zero times, so we write a zero above the line and a small 22 – the remainder – in between the 22 and the 33. Then, we see how many times 99 goes into 2323, which is 22, writing the result above the line and the remainder, 55, just before the next digit of the dividend, so we find,

 

      0  2  69)22354                ;;;0;2;6\9overline{left)2{}^23{}^54right.}\;;;;;;;;

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Specification Points Covered

Number – 2. apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers – all both positive and negative; understand and use place value (e.g. when working with very large or very small numbers, and when calculating with decimals)

Long Division – The Bus Stop Method Worksheet and Example Questions

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