The idea, step by step
Partition one factor
For 34 × 6, split thirty-four into thirty and four. Six groups of thirty give 180, and six groups of four give 24. Together they give 204. The answer stays the same because every part of every group is still counted.
You may also double and halve when it helps. For 25 × 16, double twenty-five to fifty and halve sixteen to eight; 50 × 8 is 400. Use a method you can explain rather than changing a factor without compensating.
| 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 36 × 14, split fourteen into ten and four. The two partial products are 360 and 144. Add them to get 504. In a written algorithm, the product for the tens digit must also be worth ten times as much as a ones-digit product.
An estimate helps catch a place-value mistake: 36 × 14 is close to 40 × 14 = 560, so 504 is sensible. An answer such as 180 is much too small because fourteen groups must exceed ten groups of thirty-six.
A common trap
Calculating 24 × 13 as 24 × 1 + 24 × 3.
Instead: The one in thirteen means ten. Use 24 × 10 + 24 × 3, which is 240 + 72 = 312.
See the thinking
Multiply by a one-digit number
Calculate 47 × 8 using partitioning.
- Split forty-seven into forty and seven.
- 40 × 8 = 320 and 7 × 8 = 56.
- Add 320 and 56.
Multiply by a two-digit number
A school orders 23 boxes with 18 pencils in each box. How many pencils are ordered?
- Split eighteen into ten and eight.
- 23 × 10 = 230; 23 × 8 = 184.
- Add the partial products: 230 + 184 = 414.
Check your understanding
Calculate 28 × 12. Show two partial products.
Show answer
336.
28 × 10 = 280 and 28 × 2 = 56; 280 + 56 = 336.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Calculate 62 × 4.1 mark
- Calculate 35 × 7.1 mark
- Calculate 42 × 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 × 24.2 marks
- Kai calculates 31 × 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 × 4.1 mark
60 × 4 = 240 and 2 × 4 = 8; add them.
248. - Calculate 35 × 7.1 mark
30 × 7 = 210 and 5 × 7 = 35.
245. - Calculate 42 × 16 using tens and ones.2 marks
42 × 10 = 420; 42 × 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 × 10 = 240 and 24 × 5 = 120.
240 + 120 = 360.
360 seats. - Use doubling and halving to calculate 25 × 24.2 marks
Double twenty-five to fifty and halve twenty-four to twelve.
50 × 12 = 600.
600. - Kai calculates 31 × 12 as 31 + 62 = 93. Explain the error and correct the answer.3 marks
Twelve means ten plus two.
31 × 10 + 31 × 2 = 310 + 62 = 372.
The tens contribution should be 310, so the answer is 372.
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 ↗