Methods for multiplication and division

In a nutshell

Multiplying and dividing numbers each have their own methods. The two main methods for multiplication are the grid method and the column method. The easiest method when dividing is short division (or "bus stop" method). These methods can also be applied when multiplying and dividing decimals.

Multiplication

Grid method

procedure

1.	Split up the numbers into their place values. For example: $248 = 200+40+8$
2.	Draw a grid with these place values on the top and left of the grid.
3.	Multiply each number with the others in the grid and put the answers in the corresponding box.
4.	Add up all the numbers in the boxes.

Example 1

What is $248\times35$ ?

First, write $248$ as $200+40+8$ , and $35$ as $30+5$ .

Then, as $248$ has three digits, and $35$ has 2 digits, draw a $3\times2$ grid, putting the place values around the grid as shown below:

$\times$	$\textbf{200}$	$\textbf{40}$	$\textbf{8}$
$\textbf{30}$
$\textbf{5}$

Fill in all the gaps by multiplying the numbers:

$\times$	$\textbf{200}$	$\textbf{40}$	$\textbf{8}$
$\textbf{30}$	$200\times30=6000$	$40\times30=1200$	$8\times30=240$
$\textbf{5}$	$200\times5=1000$	$40\times5=200$	$8\times5=40$

Add up all the numbers in the grid:

$6000+1200+1000+240+200+40=8680$

$\underline{248\times35=8680}$

Column method

procedure

1.	Arrange the two numbers in a column, similar to the arrangement for column addition and subtraction.
2.	Take the digit in the ones column and multiply it by the other number, writing down the answer below.
3.	Repeat this with every digit of one of the numbers, adding the correct number of zeroes to represent the place value.
4.	Add up all the numbers that have been written as a result of multiplication.

Example 2

What is $17\times34$ ?

Maths; Number calculations; KS3 Year 7; Methods for multiplication and division

$\underline{17\times34=578}$

Note: In the example above, the second line of working has a zero, as you are multiplying the number $17$ by $3\underline{0}$ .

Multiplying decimals

To multiply decimals, follow this procedure:

procedure

1.	Count how many digits past the decimal point both numbers have, and add these together.
2.	Multiply both numbers as if they were whole numbers (using the grid or column method if necessary).
3.	Move the decimal point to the left by the same amount of spaces as the number from the first step.

Example 3

What is $24.8\times0.35$ ?

First, $24.8$ has $1$ number past the decimal point, and $0.35$ has $2$ numbers past the decimal point. Adding these together gives $2+1=3$ .

Then, multiply the two numbers together as if they were whole numbers. From the first example:

$248\times35=8680$

Lastly, move the decimal point to the left three times, giving:

$24.8\times0.35=8.\overset{\curvearrowleft \curvearrowleft \curvearrowleft}{6\thinspace 8 \thinspace 0}$ 

$\underline{24.8\times0.35=8.68}$ 

Division

The "bus stop" method

The "bus stop" method for division goes as follows:

procedure

1.	Write the dividend (first number) under the "bus stop" and the divisor (second number) as follows: $128\div8 \rightarrow 8\overline{\smash{)}128}$
2.	Starting from the left-hand side of the number being divided, find how many times the divisor goes into the first digit. Write the answer on top of the line in the corresponding position.
3.	If there is a remainder, "carry over" into the column to the right of this digit. If the number cannot be divided into, read the next column as a two digit number, including the undivided digit.
4.	Repeat until the last digit has been divided. The answer is now on the top of the line.

Example 4

What is $128\div8$ ?

Maths; Number calculations; KS3 Year 7; Methods for multiplication and division

$\underline{128\div8=16}$

Dividing decimals

To divide two decimals (or a decimal and a whole number), multiply both numbers by the same power of 10 (10, 100, 1000, etc.) until both numbers are whole numbers. Then, proceed with the division as per usual.

Example 5

What is $1.28\div0.08$ ?

Multiplying both numbers by $100$ will make them whole numbers. Hence:

$1.28\div0.08=(1.28\times100)\div(0.08\times100)$ 

$1.28\div0.08=128\div8$ , which was completed in the example above.

$\underline{1.28\div0.08=16}$ 