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Dividing numbers up to 4 digits by a 2-digit number

Dividing numbers up to 4 digits by a 2-digit number

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Summary

Dividing numbers up to 4 digits by a 2-digit number

​​​​In a nutshell

​​​​​​Division is the inverse of multiplication. Four digit numbers are whole numbers between 10001000​ and 99999999. Two-digit numbers are whole numbers between 1010 and 99.99. A four digit number can be divided by a two-digit number using two methods: chunking and long division. 


Chunking

The chunking method separates four digit numbers into multiple easy to divide "chunks" in order to divide it by a two digit number. 


Example 1

Calculate: 7500÷25.7500 \div 25.


​ 75007500 can be split into two smaller "chunks" of 50005000 and 25002500.​


5000÷25=2002500÷25=100200+100=300\begin{aligned} 5000\div25 &= 200 \\ 2500\div25 &=100 \\ \\ 200+100&=300 \\ \end{aligned}


7500÷25=300 \underline{7500\div25 = 300}



Long division

Long division breaks  up a calculation into a sequence of smaller divisions which are easier to calculate. 



PROCEDURE

11​​

Write the number you are dividing by, the divisor, inside the "bus stop" and the number being divided outside as follows: 6240÷2020)62406240\div20 \rightarrow 20\overline{\smash{)}6240}.

22​​

Starting from the left-hand side of the number being divided, find how many times the divisor goes into the first digit. In this case as the divisor is two digits, it will always be greater than the first digit and therefore not divisible.    

33​​

Combine the first two digits of the number being divided and find out how many times the divisor goes into the first two digits. (If the divisor is still greater than the first two digits, repeat this step again but for the first three digits instead).

44​​

Subtract the largest multiple of the divisor which fits into the first two or three digits of the dividend and write it below. This is the remainder.

55​​

Bring down the next digit to be divided and place this to the right of the remainder. 

66​​

Repeat until all four digits have undergone division and you are left with 00 or a remainder after the final subtraction. ​



Example 2

Calculate: 6240÷206240\div 20.


Write the calculation in the long division format.


20)6  24020\overline{\smash{)}6\space\space240}


6 is not divisible by 2020 so combine the first two digits.


20)62  400  20\overset{0\quad\space\,\,\,}{\overline{\smash{)}62\space\space40}}

​​

(20×3)=60(20 \times \underline3) = 60 So 6060 is the largest multiple of 2020 which goes into 6262.

 Subtract 6060  from 6262 for the remainder.


20 )62400 3     60   2\begin{aligned} &20\space\overset{0\,\underline3\space\space\,\,}{\overline{\smash{)}6240}} \\ &-\space\,60 \\ \hline &\quad\space\space\,\,\,\,2 \end{aligned}


Bring down the next digit.


20 )62400 3     60 24\begin{aligned} &20\space\overset{0\,\underline3\space\space\,\,}{\overline{\smash{)}6240}} \\ &-\space\,60 \\ \hline &\quad\,\quad24 \end{aligned}


(20×1)=20(20 \times \underline1) = 20 . So 2020​ is the largest multiple of 2020​ which goes into 2424

Subtract 2020  from 2424 for the remainder. 


20 )6240 0 3 1    60 24    20  4\begin{aligned} &20\space\overset{\,\,\,0\,\underline3\,\underline1\space\,\,}{\overline{\smash{)}6240}} \\ &-\space\,60 \\ \hline &\quad\quad\,24 \\ &-\space\space\space\,20 \\ \hline &\quad\quad\space\,\,4 \end{aligned}


Bring down the next digit.


20 )6240 0 3 1    60 24    20  40\begin{aligned} &20\space\overset{\,\,\,0\,\underline3\,\underline1\space\,\,}{\overline{\smash{)}6240}} \\ &-\space\,60 \\ \hline &\quad\,\quad24 \\ &-\space\space\space\,20 \\ \hline &\space\quad\quad\,\,40 \end{aligned}


(20×2)=40(20\times \underline2) = 40So 4040 is the largest multiple of 2020​ which goes into 4040

Subtract 4040 from 4040.


20 )6240 0 3 1 2  60 24    20   40  40 0\begin{aligned} &20\space\overset{\,\,\,0\,\underline3\,\,\underline1\,\underline2}{\overline{\smash{)}6240}} \\ &-\space\,60 \\ \hline &\quad\,\,\,\,\,\,\,24 \\ &-\space\space\space\,20 \\ \hline &\quad\space\space\quad\,40 \\ & - \quad\,\space40 \\ \hline &\quad\quad\quad\, 0 \end{aligned}


6240÷20=312\underline{6240\div 20 = 312}


Note: Use trial and error to find the largest multiple of the divisor which will fit into the number being divided. 


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FAQs - Frequently Asked Questions

What are the main methods used to divide four digit numbers by a two digit numbers?

Why is long division used?

In long division, how do you know what to subtract at each stage?

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