Division strategies | Year 5

01 / LEARN

Understand the idea.

Split the total into useful multiples

Divide a large total by splitting it into useful multiples of the divisor. For $252 \div 6$ , use $240 + 12$ : dividing gives $40 + 2 = 42$ . The parts need not follow the digits, but must add to the original total.

You can describe the same method as removing groups. Forty groups of six use $240$ , leaving $12$ , or two more groups. Add the numbers of groups, $40 + 2$ , rather than adding the divisor again.

Partial quotients for 252 ÷ 6
Part of the total	Groups of 6
240	40
12	2
252	42

Check both the number and its meaning

Check a division by multiplying the quotient by the divisor. For $252 \div 6 = 42$ , the check $42 \times 6 = 252$ recovers the starting total. If anything is left over, include that remainder in the check as well.

The question determines what the quotient counts. Sharing $735$ beads among five groups gives beads per group; putting $735$ beads in bags of five gives a number of bags. The arithmetic matches, but the answer units differ.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Share a total

Share 735 stickers equally among five classes. How many stickers does each class get?

Worked solution

1
Split the stickers into two divisible amounts.
$735 = 700 + 35$
Both 700 and 35 can be shared exactly among five classes.
2
Share each part equally.
$700 \div 5 = 140, 35 \div 5 = 7$
Every class receives its share of both parts.
3
Combine the shares for one class.
$140 + 7 = 147$
Each class gets 147 stickers, not 147 classes.
4
Check that all stickers are accounted for.
$147 \times 5 = 735$
Five equal shares rebuild the original total.

Answer

147 stickers per class.

EXAMPLE 02

Use a nearby multiple

Calculate 364 ÷ 7.

Worked solution

1
Use a large known multiple of seven.
$50 \times 7 = 350$
350 accounts for fifty groups and is close to 364.
2
Find the leftover amount and divide it.
$364 - 350 = 14, 14 \div 7 = 2$
The remaining 14 makes two more complete groups.
3
Add the numbers of groups.
$50 + 2 = 52$
The total quotient counts all the groups removed.
4
Check by multiplication.
$52 \times 7 = 364$
The quotient and divisor reproduce the dividend with no remainder.

Answer

52.

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate 432 ÷ 8 and give a multiplication check.

Show answer & reasoning

54; 54 × 8 = 432.

Use $432 = 400 + 32$ . Then $400 \div 8 = 50$ and $32 \div 8 = 4$ , giving $54$ . The check $54 \times 8 = 432$ confirms it.

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Calculate $168 \div 4$ .
1 mark
Calculate $315 \div 5$ .
1 mark
Calculate $456 \div 6$ using partial quotients.
2 marks
A library packs 288 books equally into eight boxes. How many books are in each box?
2 marks
Calculate $624 \div 12$ using known multiples of twelve.
2 marks
Zoe says $294 \div 7 = 41$ . Use multiplication to check the claim and then correct it.
3 marks

Read the worked solutions

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

Calculate $168 \div 4$ .
1 mark
$160 \div 4 = 40$ and $8 \div 4 = 2$ .
42.
Calculate $315 \div 5$ .
1 mark
$300 \div 5 = 60$ and $15 \div 5 = 3$ .
63.
Calculate $456 \div 6$ using partial quotients.
2 marks
$420 \div 6 = 70$ and $36 \div 6 = 6$ .
76.
A library packs 288 books equally into eight boxes. How many books are in each box?
2 marks
$240 \div 8 = 30$ and $48 \div 8 = 6$ .
There are thirty-six books per box.
36 books.
Calculate $624 \div 12$ using known multiples of twelve.
2 marks
$12 \times 50 = 600$ , leaving twenty-four.
$12 \times 2 = 24$ , so the quotient is fifty-two.
52.
Zoe says $294 \div 7 = 41$ . Use multiplication to check the claim and then correct it.
3 marks
There are seven more in 294, so one more group of seven is needed.
$42 \times 7 = 294$ .
$41 \times 7 = 287$ , not 294. The correct quotient is 42.

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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.

Split the total into useful multiples

Check both the number and its meaning

See the method in action.

Share a total

Split the stickers into two divisible amounts.

Share each part equally.

Combine the shares for one class.

Check that all stickers are accounted for.

Use a nearby multiple

Use a large known multiple of seven.

Find the leftover amount and divide it.

Add the numbers of groups.

Check by multiplication.

Try it yourself.

Check your understanding

Keep practising