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 $1000$ and $9999$ . 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: $2500 \div 5.$

$2500$ can be split into two smaller "chunks" of $2000$ and $500$ .

$\begin{aligned} 2000\div5 &= 400 \\ 500\div5&=100 \\ \\ 400+100&=500 \\ \end{aligned}$

$2500\div5 = \underline{500}$

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

Short division

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

PROCEDURE

$1$	Write the number your are dividing by under the "bus stop" and the number being divided as follows: $5000\div5 \rightarrow 5\overline{\smash{)}5000}$ .
$2$	Starting from the left-hand side of the number being divided, find how many times the divisor goes into the first digit.
$3$	Write the answer above the "bus stop" and carry over any remainders to the next digit.
$4$	Repeat the procedure for the next digit.

Example 2

Calculate: $5740 \div 4 .$

Write $4$ outside the bus stop and $5740$ inside the bus stop. Begin by finding how many $4$ s go into $5$ .

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

$5 \div 4= 1\space remainder \ 1$

Write the answer $1$ above $5$ . Write the remainder $1$ in front of $7$ . Work out how many $4$ s go into $17$ .

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

$17\div 4 = 4\space remainder\space 1$

Write the answer $4$ above $7$ . Write the remainder $1$ in front of $4$ . Work out how many $4$ s go into $14$ .

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

$14 \div 4 = 3 \space remainder \space 2$

Write the answer $3$ above $4$ . Write the remainder $2$ before $0$ . Lastly, work out how many $4$ s go in $20$ .

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

$20\div 4 = 5$

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

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

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: $1004\div5.$

$1004$ can be split into three smaller "chunks" of $500$ and $500$ and $4$ .

$\begin{aligned} 500\div5 &= 100 \\ 500\div5&=100 \\ \\ 100+100&=200 \\ \end{aligned}$

$4$ is not divisible by $5$ .

$1004\div5 = \underline{200\space remainder\space 4}$

Example 4

Use short division to solve: $3964\div3$ .

Write $3$ outside the bus stop and $3964$ inside the bus stop.

$3{\overline{\smash{)}3964}}$ 

Find how many $3$ 's first fit into $3$ , $9$ and $6$ . Write the answers, $1$ , $3$ and $2$ above each number respectively.

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

$4$  is not wholly divisible by $3$ .

Find the largest whole division you can perform.

$3\div3=1$

Write $1$ above $4$ .

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

Find the remainder.

$\begin{aligned} 3\times1 = 3 \\ 4-3=1 \end{aligned}$

$3964\div3 = \underline{1321\space remainder\space 4}$