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 $1000$ and $9999$ . Two-digit numbers are whole numbers between $10$ and $99.$ 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: $7500 \div 25.$

$7500$ can be split into two smaller "chunks" of $5000$ and $2500$ .

$\begin{aligned} 5000\div25 &= 200 \\ 2500\div25 &=100 \\ \\ 200+100&=300 \\ \end{aligned}$

$\underline{7500\div25 = 300}$

Long division

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

PROCEDURE

$1$	Write the number you are dividing by, the divisor, inside the "bus stop" and the number being divided outside as follows: $6240\div20 \rightarrow 20\overline{\smash{)}6240}$ .
$2$	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.
$3$	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).
$4$	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.
$5$	Bring down the next digit to be divided and place this to the right of the remainder.
$6$	Repeat until all four digits have undergone division and you are left with $0$ or a remainder after the final subtraction.

Example 2

Calculate: $6240\div 20$ .

Write the calculation in the long division format.

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

6 is not divisible by $20$ so combine the first two digits.

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

$(20 \times \underline3) = 60$ . So $60$ is the largest multiple of $20$ which goes into $62$ .

Subtract $60$ from $62$ for the remainder.

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

Bring down the next digit.

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

$(20 \times \underline1) = 20$ . So $20$ is the largest multiple of $20$ which goes into $24$ .

Subtract $20$ from $24$ for the remainder.

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

Bring down the next digit.

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

$(20\times \underline2) = 40$ . So $40$  is the largest multiple of $20$ which goes into $40$ .

Subtract $40$ from $40$ .

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

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

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