One-/two-digit multipliers | Year 5

01 / LEARN

Understand the idea.

Partition one factor

Partial products are the results of multiplying separate parts of a number. For $34 \times 6$ , split $34$ into $30 + 4$ , multiply both parts by $6$ , then combine $180 + 24 = 204$ . Every part must be multiplied because every group contains both parts.

Another useful exchange is to double one factor and halve the other. In $25 \times 16 = 50 \times 8 = 400$ , each group doubles while the number of groups halves. The product stays the same because the two changes balance.

Partial products for 34 × 6
Part of 34	Multiply by 6	Product
30	30 × 6	180
4	4 × 6	24
Total	180 + 24	204

A tens digit means groups of ten

For a two-digit multiplier, split tens from ones. In $36 \times 14$ , the $1$ means ten, so find ten groups of $36$ and four groups of $36$ . The products are $360$ and $144$ , giving $504$ altogether.

Check the size as well as the addition. Fourteen groups of $36$ must be more than ten groups, or $360$ , and less than twenty groups, or $720$ . These bounds help catch a missing tens-place product.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Multiply by a one-digit number

Calculate 47 × 8 using partitioning.

Worked solution

1
Partition forty-seven into tens and ones.
$47 \times 8 = (40 \times 8) + (7 \times 8)$
Eight groups of 47 contain eight groups of 40 and eight groups of 7.
2
Calculate the partial products.
$40 \times 8 = 320, 7 \times 8 = 56$
Place value turns the known fact 4 times 8 into 40 times 8.
3
Combine both parts.
$320 + 56 = 376$
Adding the partial products counts all eight groups without omissions.

Answer

376.

EXAMPLE 02

Multiply by a two-digit number

A school orders 23 boxes with 18 pencils in each box. How many pencils are ordered?

Worked solution

1
Represent the total as equal groups.
$23 \times 18$
There are 23 boxes and each contributes 18 pencils.
2
Split eighteen into ten and eight.
$23 \times 18 = (23 \times 10) + (23 \times 8)$
Each box contributes 10 pencils and another 8 pencils.
3
Calculate both partial products.
$23 \times 10 = 230, 23 \times 8 = 184$
The tens part and ones part must both be included.
4
Add and state the unit.
$230 + 184 = 414$
The two parts together give 414 pencils.

Answer

414 pencils.

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate 28 × 12. Show two partial products.

Show answer & reasoning

336.

Split $12$ into $10 + 2$ . The partial products are $28 \times 10 = 280$ and $28 \times 2 = 56$ , so $280 + 56 = 336$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Calculate $62 \times 4$ .
1 mark
Calculate $35 \times 7$ .
1 mark
Calculate $42 \times 16$ using tens and ones.
2 marks
A theatre has 24 rows with 15 seats in each row. How many seats are there?
2 marks
Use doubling and halving to calculate $25 \times 24$ .
2 marks
Kai calculates $31 \times 12$ as $31 + 62 = 93$ . Explain the error and correct the answer.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Calculate $62 \times 4$ .
1 mark
$60 \times 4 = 240$ and $2 \times 4 = 8$ ; add them.
248.
Calculate $35 \times 7$ .
1 mark
$30 \times 7 = 210$ and $5 \times 7 = 35$ .
245.
Calculate $42 \times 16$ using tens and ones.
2 marks
$42 \times 10 = 420$ ; $42 \times 6 = 252$ .
$420 + 252 = 672$ .
672.
A theatre has 24 rows with 15 seats in each row. How many seats are there?
2 marks
$24 \times 10 = 240$ and $24 \times 5 = 120$ .
$240 + 120 = 360$ .
360 seats.
Use doubling and halving to calculate $25 \times 24$ .
2 marks
Double twenty-five to fifty and halve twenty-four to twelve.
$50 \times 12 = 600$ .
600.
Kai calculates $31 \times 12$ as $31 + 62 = 93$ . Explain the error and correct the answer.
3 marks
Twelve means ten plus two.
$31 \times 10 + 31 \times 2 = 310 + 62 = 372$ .
The tens contribution should be 310, so the answer is 372.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

One-/two-digit multipliers; division strategies; contextual remainders; inverse fact families; unknown factors/dividends/divisors.

Official curriculum source ↗

In this lesson

Understand the idea.

Partition one factor

A tens digit means groups of ten

See the method in action.

Multiply by a one-digit number

Partition forty-seven into tens and ones.

Calculate the partial products.

Combine both parts.

Multiply by a two-digit number

Represent the total as equal groups.

Split eighteen into ten and eight.

Calculate both partial products.

Add and state the unit.

Try it yourself.

Check your understanding

Keep practising