Multiplying and dividing whole numbers

​​In a nutshell

You can use both long and short division and multiplication to solve multiplying and dividing calculations when a calculator is not available.

Multiplication

Definitions

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Procedure

Example 1

Calculate $$387 \times 56$$ using long multiplication.

Set out the calculation.

$$\begin{array}{ccccc}&\text{TTh}&\text{Th} & \text{H} & \text{T} & \text{O} \\& & & 3 &8 & 7 \\\times & & & &5& 6 \\ \hline \\+ \\ \hline \end{array}$$​​

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Multiply each digit of $$387$$ by $$6$$.

$$\begin{array}{ccccc}&\text{TTh}&\text{Th} & \text{H} & \text{T} & \text{O} \\& & & 3 &8 & 7 \\\times & & & &5& 6 \\ \hline& &^22&^53&^42&2 \\+ \\ \hline& \end{array}$$​​

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Then by $$5$$, adding a $$0$$ in the units column.

$$\begin{array}{ccccc}&\text{TTh}&\text{Th} & \text{H} & \text{T} & \text{O} \\& & & 3 &8 & 7 \\\times & & & &5& 6 \\ \hline& &^22&^53&^42&2 \\+ &^11&^49&^33&5&0\\ \hline&&&&& \end{array}$$​​

Add the results.

​$$\begin{array}{ccccc}&\text{TTh}&\text{Th} & \text{H} & \text{T} & \text{O} \\& & & 3 &8 & 7 \\\times & & & &5& 6 \\ \hline& &^22&^53&^42&2 \\+& ^11&^49&^33&5&0 \\ \hline& 2&1&6&7&2 \end{array}$$​

$$387 \times 56=\underline{21\space672}$$​​

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Note: Multiplying by a single-digit number in the same way is known as short multiplication. Long multiplication involves adding two or more result of calculations and is used for larger-digit numbers, like you can see used above.

Division

Long division and short division are both methods of dividing one number by another. Long division involves writing down each step of the calculation, whereas short division is done mentally and each step is not written down.

Definitions

Short division

To use short division, you must be able to divide each column by the divisor. Either you need to know the times tables for it, or you can write out a list of its multiples.

Procedure

Note: If you still have a remainder when you divide the units of the dividend, add a decimal place and a zero to the next column and carry the remainder. Repeat until there is no remainder left and add a decimal place in the correct column to your final answer.

Example 2

Calculate $$1020\div8$$ using short division.

Set out the calculation.

$$8\overset{}{\overline{\smash{)}1\,0\,2\,0}} \\$$​​

Since $$1$$​ cannot divide $$8$$​, carry the $$1$$ to the next column and divide.

$$8\overset{\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,}{\overline{\smash{)}\cancel1^1020}} \\$$

Continue carrying and dividing each column.

​$$8\overset{\,\,\,\,\,\,\,\,\,\,1\,\,\,\,2\,\,\,\,7.\,\,\,5}{\overline{\smash{)}\cancel1^10^22^60.^40}}$$​​

​$$1020\div8=\underline{127.5}$$

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