Written Methods of Multiplication

Multiply whole numbers on paper: split by place value, use the column method with carries, copy a given method, and check the answer is the right size.

In the exam for Cambridge IGCSE Maths 0580, Cambridge O Level Maths 4024, Edexcel IGCSE Maths 4MA1 · 5 real past-paper questions below

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Splitting a Product by Place Value

A written method splits one number into hundreds, tens and units. You multiply each piece, then add the pieces back together.

Worked example

1
$47 \times 6 = 40 \times 6 + 7 \times 6$ — split 47 into 40 and 7
2
$= 240 + 42$ — forty sixes, then seven sixes
3
$= 282$ — add the pieces

Key idea

Every layout you meet, columns or a grid, is this one idea: split, multiply each piece, add.

Column Method: One Digit

The 1-mark question: work out a product like $384 \times 7$ with no calculator. Start with the units and go left, carrying as you go.

Worked example

1
$4 \times 7 = 28$ — write 8, carry 2
2
$8 \times 7 = 56, 56 + 2 = 58$ — add the carry after you multiply: write 8, carry 5
3
$3 \times 7 = 21, 21 + 5 = 26$ — write 26 at the front
4
$384 \times 7 = 2688$ — read the answer

Common mistake

Adding the carry before multiplying. $(8 + 2) \times 7$ is wrong. Multiply first, then add the carry.

Long Multiplication

The 2-mark question: work out $384 \times 27$ without a calculator. Multiply by each digit of 27 on its own row, then add the rows.

Worked example

1
$384 \times 7 = 2688$ — row 1: the units digit
2
$384 \times 20 = 7680$ — row 2: the 2 is worth 20, so write a 0 first
3
$2688 + 7680 = 10368$ — add the two rows

Common mistake

Leaving out the 0 on row 2. Then you add 768, not 7680, and get 3456: far too small.

Memory trick

Row 2 starts with a 0 because you are multiplying by tens. Hundreds would need two zeros.

Use the Given Method

The 2-mark question shows someone's method, such as $53 \times 99 = 5300 - 53$ . Copy the same steps with the new numbers.

Worked example

1
$76 \times 99 = 76 \times 100 - 76$ — 99 is one less than 100
2
$= 7600 - 76$ — take away one lot of 76
3
$= 7524$ — the answer

The same idea works with a fact you are given. If $36 \times 25 = 900$ , then one more 36 is next.

Worked example

1
$36 \times 26 = 900 + 36$ — 26 lots is 25 lots plus one more
2
$= 936$ — the answer

Common mistake

Taking away 99 or 1 instead of 76. You took 100 lots of 76, so remove one lot of 76.

Cost Problems Without a Calculator

The 1-mark or 2-mark question: a price times a number of items. Multiply, then give the answer in the units asked for.

A pen costs 65 cents. Find the cost of 14 pens, in dollars.

Worked example

1
$65 \times 14 = 65 \times 10 + 65 \times 4$ — split 14 into 10 and 4
2
$= 650 + 260 = 910$ — 910 cents
3
$910 cents = $9.10$ — 100 cents make a dollar

Common mistake

Writing $910. Check the units: the price was in cents, the answer is wanted in dollars.

Is the Answer the Right Size?

A written method can go wrong quietly. A quick estimate catches it.

Rule

Round each number to 1 significant figure, multiply, and check your answer is close.

Worked example

1
$384 \times 27 \approx 400 \times 30$ — round each number
2
$= 12000$ — the estimate
3
$10368 is close: sensible$ — 3456 would not be

Key idea

The estimate only has to catch an answer that is ten times too big or too small. That is the slip a missing 0 makes.

Which Method? Read the Question

The words in the question tell you which method to use.

You see	You do
Times a single digit	column method, carry as you go
Two-digit times two-digit or more	long multiplication, one row per digit
Use this method	copy each step with the new numbers
Price of several items	multiply, then check the units
Is the answer sensible?	round each number, see Estimation
Decimals, like 3.6 × 0.4	Adding, Subtracting, Multiplying and Dividing Decimals

Key idea

In 1202 Fibonacci's book Liber Abaci showed European merchants how to calculate with the digits 0 to 9 instead of Roman numerals. The column methods here grew from that change.

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Real past-paper questions on written methods of multiplication

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