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

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 $$20$$.

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

​​$$20\div 4 = 5$$

​​

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

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

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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. 

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

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

Find the largest whole division you can perform.

 $$3\div3=1$$

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Write $$1$$ above $$4$$.

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

Find the remainder.

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

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