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Dividing numbers up to 4 digits by a 1-digit number

Dividing numbers up to 4 digits by a 1-digit number

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Summary

Dividing numbers up to 4 digits by a 1-digit number

​​​​In a nutshell

Division is the inverse of multiplication. Four digit numbers are whole numbers between 10001000​ and 99999999. They can primarily be divided by a one-digit number using two methods: chunking and short division. 



Chunking

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


Example 1

Calculate: 2500÷5.2500 \div 5.

​ 25002500 can be split into two smaller "chunks" of 20002000 and 500500.​

2000÷5=400500÷5=100400+100=500\begin{aligned} 2000\div5 &= 400 \\ 500\div5&=100 \\ \\ 400+100&=500 \\ \end{aligned} ​​


2500÷5=5002500\div5 = \underline{500}


Note: Use chunking for simple four digit numbers such as: 1000,4500,80001000, 4500, 8000.



Short division

Short division is also known as the "bus stop" method. To perform short division:


PROCEDURE

11​​

Write the number your are dividing by under the "bus stop" and the number being divided as follows: 5000÷55)50005000\div5 \rightarrow 5\overline{\smash{)}5000}.

22​​

Starting from the left-hand side of the number being divided, find how many times the divisor goes into the first digit.   

33​​

Write the answer above the "bus stop" and carry over any remainders to the next digit. 

44​​

Repeat the procedure for the next digit.



Example 2

Calculate: 5740÷4.5740 \div 4 .


Write 44 outside the bus stop and 57405740 inside the bus stop. Begin by finding how many 44s go into 55.

4)57404\overline{\smash{)}5740}

5÷4=1 remainder 15 \div 4= 1\space remainder \ 1


Write the answer 11 above 55. Write the remainder 11 in front of 77. Work out how many 44s go into 1717.

4)5 1 ⁣7401 4\overset{1\,\,\,\,\,\,\,\,\,\,\,\,}{\overline{\smash{)}5~^1\!740}}

17÷4=4 remainder 117\div 4 = 4\space remainder\space 1

​​

Write the answer 44 above 77. Write the remainder 11 in front of 44. Work out how many 44s go into 1414.

4)57 1 ⁣40 1 4 4\overset{\,\,1\,\,4\,\,\,\,\,\,\,\,\,\,}{\overline{\smash{)}57~^1\!40}}

14÷4=3 remainder 214 \div 4 = 3 \space remainder \space 2


Write the answer 33 above 44. Write the remainder 22 before 00. Lastly, work out how many 44s go in 2020.

4)574 2 ⁣0 1 4 3 4\overset{\,\,\,1\,\,4\,\,3\,\,\,\,\,\,\,\,}{\overline{\smash{)}574~^2\!0}}​​

​​20÷4=520\div 4 = 5

​​

4)574  ⁣0 1 4 3 5 4\overset{\,\,\,1\,\,4\,\,3\,\,5\,}{\overline{\smash{)}574~\!0}}


5740÷5=1435 5740 \div 5 = \underline{1435}

​​


Remainders

One-digit numbers do not always fit into a four digit number. The amount which is left over after division is known as a remainder. 


Example 3

Use the chunking method to solve: 1004÷5.1004\div5.


10041004 can be split into three smaller "chunks" of 500500​​ and 500500 and 44.


500÷5=100500÷5=100100+100=200\begin{aligned} 500\div5 &= 100 \\ 500\div5&=100 \\ \\ 100+100&=200 \\ \end{aligned}

44​ is not divisible by 55​.


1004÷5=200 remainder 41004\div5 = \underline{200\space remainder\space 4}



Example 4

Use short division to solve: 3964÷33964\div3.


Write 33 outside the bus stop and 39643964​ inside the bus stop. 

3)39643{\overline{\smash{)}3964}}​​


Find how many 33​'s first fit into 33​, 99​ and 66​. Write the answers, 11​, 33​ and 22​ above each number respectively. 

3)3964 1 3 2 3\overset{\,\,\,\,1\,3\,\,2\,\,\,\,}{\overline{\smash{)}3964}}

44​ is not wholly divisible by 33.

Find the largest whole division you can perform.

 3÷3=13\div3=1

​​

Write 11 above 44.

3)3964 1 3 2 1 3\overset{\,\,\,\,1\,3\,\,2\,\,1\,\,}{\overline{\smash{)}3964}}​​


Find the remainder.

3×1=343=1\begin{aligned} 3\times1 = 3 \\ 4-3=1 \end{aligned}​​


3964÷3=1321 remainder 43964\div3 = \underline{1321\space remainder\space 4} ​​


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