The idea, step by step
Partition larger numbers
A known fact can be scaled to tens or hundreds. Since 6 × 2 = 12, 6 × 20 = 120. To find 6 × 23, split 23 into 20 + 3. Multiply each part, then add the two results.
Division can also use useful parts. For 156 ÷ 3, split 156 into 150 + 6. Both parts divide easily by 3. The two quotients are 50 and 2, making 52 altogether. Choose parts that fit the divisor.
A remainder must fit the situation
Some amounts do not split into the requested groups exactly. For 86 ÷ 4, twenty-one groups use 84, leaving 2. Write 21 remainder 2. The leftover must be smaller than the divisor: another full group would otherwise be possible.
Check by rebuilding the total: divisor × quotient + remainder. In a story, a remainder can mean items left over, or a need for an extra container. Say which meaning fits rather than simply writing the remainder without a unit.
A common trap
For 24 × 3, multiplying only the 4 ones and answering 12.
Instead: Multiply both place-value parts: 20 × 3 = 60 and 4 × 3 = 12, so 24 × 3 = 72.
See the thinking
Multiply in parts
Find 23 × 6.
- Split 23 into 20 + 3.
- 20 × 6 = 120 and 3 × 6 = 18.
- 120 + 18 = 138.
Divide and interpret
86 counters are shared equally among 4 pupils. How many does each get, and how many remain?
- 4 × 20 = 80, leaving 6.
- One more counter each uses 4 of those 6, leaving 2.
- Check: 4 × 21 + 2 = 86.
Check your understanding
Find 152 ÷ 4 using 120 + 32.
Show answer
38.
120 ÷ 4 = 30 and 32 ÷ 4 = 8, so the quotient is 38.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- Find 34 × 3.1 mark
- Find 46 × 5.1 mark
- Find 168 ÷ 4.1 mark
- Find 246 ÷ 3.1 mark
- Put 95 apples into full bags of 6. How many full bags can be made, and how many apples remain?2 marks
- A coach must seat 47 pupils in minibuses with 8 pupil seats each. How many minibuses are needed? Explain the remainder.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find 34 × 3.1 mark
30 × 3 = 90; 4 × 3 = 12.
90 + 12 = 102.
102. - Find 46 × 5.1 mark
40 × 5 = 200; 6 × 5 = 30.
200 + 30 = 230.
230. - Find 168 ÷ 4.1 mark
160 ÷ 4 = 40; 8 ÷ 4 = 2.
40 + 2 = 42.
42. - Find 246 ÷ 3.1 mark
240 ÷ 3 = 80; 6 ÷ 3 = 2.
80 + 2 = 82.
82. - Put 95 apples into full bags of 6. How many full bags can be made, and how many apples remain?2 marks
6 × 15 = 90.
95 − 90 = 5; the remainder is less than 6.
15 full bags and 5 apples left. - A coach must seat 47 pupils in minibuses with 8 pupil seats each. How many minibuses are needed? Explain the remainder.2 marks
47 ÷ 8 = 5 remainder 7.
Five minibuses seat only 40 pupils. The other 7 need one more minibus.
6 minibuses.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.
Official curriculum source ↗