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

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.