Singapore Math multiplication and division guide for families and teachers outside Singapore: what Primary 1 to Primary 5 students learn, the written methods, and how to practise at home.
Multiplication puts equal groups together.
Division splits a whole into equal groups.
In Singapore Mathematics, students start with small numbers in Primary 1 and learn the tables in Primary 2 and Primary 3. In Primary 4, written methods reach 4 digits by 1 digit for both operations, and 3 digits by 2 digits for multiplication.
In Primary 5, students multiply and divide by 10, 100, 1000 and their multiples without a calculator, and learn the order of operations.
This guide is useful for families and teachers who want to:
- know the exact limits at each level;
- teach the written methods with understanding;
- prepare a child who is moving into a Singapore school; or
- support a student using Singapore Math materials in another country.
Quick facts
Level: Primary 1 to Primary 5 (Standard Mathematics)
Strand: Number and Algebra
Official source: MOE Primary Mathematics Syllabus, the 2021 syllabus first examined at PSLE in 2026
Comes after: Multiplication Tables
Leads to: Factors and Multiples and Order of Operations
What Multiplication and Division Mean in Singapore Mathematics
Multiplication combines equal groups. 4 × 6 can show 4 groups of 6 or 6 groups of 4.
Division has two meanings. Sharing asks how many are in each group. Grouping asks how many groups can be made. 24 ÷ 4 answers both kinds of question.
The two operations undo each other. The syllabus lists “the relationship between multiplication and division” in Primary 2.
Written methods rest on place value. 346 × 27 is 346 × 20 plus 346 × 7. Long division works one place at a time, from the greatest place down.
When a division does not come out exactly, the amount left over is the remainder. It must be smaller than the divisor.
Where Multiplication and Division Sit in the Singapore Syllabus
| Level | Multiplication | Division |
|---|---|---|
| Primary 1 | Concepts; the × symbol; multiplying within 40 | Dividing within 20 |
| Primary 2 | Tables of 2, 3, 4, 5 and 10, including mentally | The ÷ symbol; dividing within these tables |
| Primary 3 | Tables of 6, 7, 8 and 9; algorithms up to 3 digits by 1 digit | Division with remainder; algorithms up to 3 digits by 1 digit |
| Primary 4 | Algorithms up to 4 digits by 1 digit and up to 3 digits by 2 digits | Algorithm up to 4 digits by 1 digit |
| Primary 5 | Multiplying by 10, 100, 1000 and their multiples, without calculator | Dividing by 10, 100, 1000 and their multiples, without calculator |
Primary 2 also names the relationship between the two operations, and Primary 3 adds mental calculation within the tables.
In Primary 4, the operations reach decimals: multiplying and dividing decimals (up to 2 decimal places) by a 1-digit whole number, and dividing a whole number by a whole number with the quotient as a decimal.
Primary 5 adds the order of operations and brackets, “without calculator”, and dividing a whole number by a whole number with the quotient as a fraction.
The written division algorithm in the syllabus stops at 1-digit divisors. In Primary 5, students also divide by 10, 100, 1000 and their multiples, such as 4800 ÷ 60.
In Primary 5 Foundation Mathematics, the multiplication and division algorithms are revisited up to 2 digits by 1 digit, “without calculator”.
How Singapore Teaches Multiplication and Division
1. Equal groups and sharing
Children share objects fairly and count groups. The story comes before the symbol.
2. Fact families
Each table fact is learned with its division facts, so 6 × 7 = 42 also gives 42 ÷ 7 = 6.
3. Multiply by splitting the number
346 × 7 is 300 × 7, 40 × 7 and 6 × 7 added together. The written method records the same steps in columns.
4. Divide one place at a time
Long division starts with the greatest place. Anything left over is renamed into the next place down.
5. Make sense of remainders
In a word problem, a remainder may mean rounding up (one more bus), rounding down (full boxes only) or simply reporting what is left.
6. Multiply and divide by 10, 100 and 1000
In Primary 5, students see the digits move through the places. 36 × 100 = 3600, and 3600 ÷ 100 = 36.
Worked Examples
3 digits by 2 digits (Primary 4)
Question: Work out 346 × 27.
Step 1. 346 × 7 = 2422.
Step 2. 346 × 20 = 6920. The zero is there because we are multiplying by 2 tens.
Step 3. 2422 + 6920 = 9342.
Check: 27 × 346 = 27 × 300 + 27 × 46 = 8100 + 1242 = 9342.
4 digits by 1 digit (Primary 4)
Question: Work out 5274 ÷ 6.
Step 1. 5 thousands cannot be shared into 6 groups of a thousand, so rename them as 50 hundreds. With the 2 hundreds, that makes 52 hundreds.
Step 2. 52 hundreds ÷ 6 = 8 hundreds, remainder 4 hundreds.
Step 3. 4 hundreds = 40 tens. With the 7 tens, that makes 47 tens. 47 tens ÷ 6 = 7 tens, remainder 5 tens.
Step 4. 5 tens = 50 ones. With the 4 ones, that makes 54 ones. 54 ÷ 6 = 9 ones.
Step 5. The answer is 879.
Check: 6 × 879 = 5274.
Common Mistakes
- Forgetting the zero when multiplying by tens. 346 × 20 is written as 692. Fix: say “times 2 tens” and write the zero first.
- Dropping a zero in the quotient. 3627 ÷ 9 is given as 43 instead of 403. Fix: when a place cannot be divided, write 0 in that place before moving on.
- A remainder that is too big. 47 ÷ 6 is given as 6 remainder 11. Fix: the remainder must be less than the divisor, so the answer is 7 remainder 5.
- Ignoring the context of a remainder. 100 pupils in vans of 8 gives “12 remainder 4 vans”. Fix: decide what the remainder means. Here 13 vans are needed.
- Choosing the wrong operation. In word problems, the child multiplies when the question asks for equal shares. Fix: draw the groups before choosing.
- Moving the wrong way with 10, 100 and 1000. 4500 ÷ 100 is given as 450 000. Fix: dividing makes the number smaller, so the digits move to lower places: 45.
Teaching Multiplication and Division Outside Singapore
- Layouts vary. Long division and column multiplication are set out differently in different countries. The place-value reasoning is the same, so keep one layout and explain why it works.
- Remainders. This guide writes “7 remainder 5”. You may also see “7 r 5” or “7 R5”.
- Limits. In the Singapore syllabus, written division stops at 1-digit divisors, and written multiplication at 3 digits by 2 digits. If your local curriculum goes further, the same place-value method extends.
- Timing. Use the Singapore Math Grade Levels guide rather than converting ages.
- Calculators. The Primary 5 work with 10, 100 and 1000 is marked “without calculator”, and PSLE Paper 1 does not allow calculators.
How to Practise Multiplication and Division at Home
- Warm up with five mixed table facts.
- Do one written multiplication and check it against an estimate.
- Do one written division and check it by multiplying back.
- Solve one remainder word problem and say what the remainder means.
- From Primary 5, practise multiplying and dividing by 10, 100 and 1000 mentally.
- Once a week, mix multiplication and division problems so the child must choose the operation.
Fifteen focused minutes is enough.
Try These
- Work out 268 × 34.
- Work out 3627 ÷ 9.
- 100 pupils travel in vans. Each van carries 8 pupils. How many vans are needed?
- Work out 23 × 300 and 4800 ÷ 60.
Answers
- 9112. 268 × 4 = 1072 and 268 × 30 = 8040, so the total is 1072 + 8040 = 9112.
- 403. 36 hundreds ÷ 9 = 4 hundreds. 2 tens ÷ 9 = 0 tens, with 2 tens left. 27 ones ÷ 9 = 3 ones.
- 13 vans. 100 ÷ 8 = 12 remainder 4, and the 4 pupils left over need a van too.
- 6900 and 80. 23 × 3 = 69, then multiply by 100. 4800 ÷ 60 gives the same answer as 480 ÷ 6, which is 80.
What Comes Next
- Factors and Multiples uses division to test whether one number divides another exactly.
- Order of Operations sets the Primary 5 rules for mixing all four operations.
- Fractions and Division shows that a division can be written as a fraction.
- Decimals extends multiplication and division to decimal numbers.
A child who understands why the written methods work can extend them with confidence.
Frequently Asked Questions
When do Singapore students learn multiplication and division?
From Primary 1, with small numbers. The tables come in Primary 2 and 3, written methods grow through Primary 3 and 4, and Primary 5 adds work with 10, 100 and 1000.
How large are the numbers in written methods?
Up to 3 digits by 1 digit in Primary 3. In Primary 4, up to 4 digits by 1 digit for both operations, and up to 3 digits by 2 digits for multiplication.
Do primary students do long division by 2-digit numbers?
The written division algorithm in the syllabus goes up to 4 digits by 1 digit. In Primary 5, students also divide by 10, 100, 1000 and their multiples.
When are remainders introduced?
In Primary 3, as “division with remainder”.
Can a calculator be used?
Not for the Primary 5 work with 10, 100 and 1000, which is marked “without calculator”. At the PSLE, calculators are allowed only in Paper 2.
When do decimals come in?
In Primary 4, students multiply and divide decimals with up to 2 decimal places by a 1-digit whole number.
Helpful Reading
- Singapore Mathematics | International Edition: Multiplication Tables
- Singapore Mathematics | International Edition: Factors and Multiples
- Singapore Mathematics | International Edition: Order of Operations
- Primary Mathematics: Equal Groups, Division and Remainders | Worked Learning Guide
- Arithmetic Operations | Mathematics Knowledge Object
- P4 Mathematics Tuition | When Knowing a Method Is No Longer Enough
- MOE Primary Mathematics Syllabus
- SEAB PSLE Formats Examined in 2026
Multiplication and Division in Singapore Mathematics
Equal groups, two ways round.
Fact families, not single facts.
Split by place value to multiply.
Divide one place at a time.
Ask what the remainder means.
By Primary 4, these steps carry 4-digit numbers.
By Primary 5, they connect to fractions, decimals and the order of operations.
Ask Bukit Timah Tutor
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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.
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