Numbers · Lesson 12 of 36

Multiplying Larger Numbers

Split a big number into tens and ones, multiply each part, and add the pieces. The column method does the same thing in a shorter layout.

Primary
Updated 14 November 2026

What you will learn

Multiply a two- or three-digit number by a one-digit number by splitting it into parts.
Multiply by a two-digit number with the area model.
Estimate first so you can check your answer.

Before you start: you should know your times tables and column addition. See Multiplication: Equal Groups and Arrays and Column Addition.

The idea

When the numbers get bigger, multiplying in your head gets harder. The trick is to break one number into parts that are easy to multiply, multiply each part, and add the results. The partial answers are called partial products.

Split into tens and ones

For $23 \times 4$ , split $23$ into $20 + 3$ . Then multiply each part by $4$ and add.

One block of 4 rows of 10 is 40. For 23 × 4 you need two of these blocks (80) and 3 more columns of 4 (12). Together 80 + 12 = 92.

$23 \times 4 = (20 \times 4) + (3 \times 4) = 80 + 12 = 92$ .

The area model

A rectangle shows the same idea. For $14 \times 12$ , split both numbers: $14 = 10 + 4$ and $12 = 10 + 2$ . Four boxes appear, and you add their areas.

The four partial products of 14 × 12: 100, 20, 40 and 8. They add to 168.

$100 + 20 + 40 + 8 = 168$ . You can also just split one number: $14 \times 12 = 10 \times 12 + 4 \times 12 = 120 + 48 = 168$ .

The column method

The column method writes the same partial products in a shorter layout. Multiply the ones first, carry if needed, then the tens, and so on. For $23 \times 4$ : $3 \times 4 = 12$ , write $2$ and carry $1$ ; $2 \times 4 = 8$ , plus the carried $1$ is $9$ . The answer is $92$ .

Adding the two partial products of 23 × 4: 80 and 12. The sum is 92.

Multiplying by tens

To multiply by $20$ , multiply by $2$ and then by $10$ (move each digit one place left). $27 \times 20$ : $27 \times 2 = 54$ , then $540$ .

Estimate first

Round to get a quick answer and compare. $49 \times 6 \approx 50 \times 6 = 300$ . The exact answer, $294$ , is close, so it looks right.

Worked examples

Example 1: Two-digit by one-digit

Work out $38 \times 5$ .

Split $38$ into $30 + 8$ .
$30 \times 5 = 150$ and $8 \times 5 = 40$ .
$150 + 40 = 190$ .

Answer: $190$ . Estimate: $40 \times 5 = 200$ .

Example 2: Three digits

Work out $314 \times 3$ .

$300 \times 3 = 900$ .
$10 \times 3 = 30$ .
$4 \times 3 = 12$ .
$900 + 30 + 12 = 942$ .

Answer: $942$ .

Example 3: Two-digit by two-digit

Work out $23 \times 15$ .

$23 \times 10 = 230$ .
$23 \times 5 = 115$ (because $20 \times 5 = 100$ and $3 \times 5 = 15$ ).
$230 + 115 = 345$ .

Answer: $345$ . Estimate: $20 \times 15 = 300$ .

Do not forget the zeros when you multiply by tens. $23 \times 40$ is $920$ , not $92$ .

Why it matters

Multiplying large numbers lets you work out totals, areas and prices that are too big to count one by one. The idea of splitting into parts is also the heart of algebra, where $(x + 3)(x + 4)$ is expanded in the same way.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.