Multiplication and division: short and long methods
Long multiplication and long division are the heavyweight methods of Year 6, and they carry two marks each on the SATs arithmetic paper. Getting them right depends on place value, times tables and tidy working.
Multiplying and dividing by 10, 100 and 1,000
When a number is multiplied by 10, every digit moves one place to the left and the number becomes ten times bigger. Dividing by 10 moves every digit one place to the right. For 100 and 1,000 the digits move two and three places.
- 3.4 × 10 = 34Each digit moves one place left.
- 3.4 × 10 = 3.40“Just add a zero” doesn't work with decimals.
- 5,600 ÷ 100 = 56Each digit moves two places right.
The “add a zero” shortcut is worth unteaching early, because it breaks the moment decimals appear. A place value chart with the digits physically sliding makes the real process clear, and it connects straight to converting units (2.5 km = 2,500 m).
Short multiplication
Short multiplication multiplies a number by a single digit in columns, carrying as needed. It's quick and reliable once times tables are secure. Most errors come from adding the carried digit before multiplying instead of after.
Long multiplication
Long multiplication multiplies by a two-digit number by finding two partial products, one for the ones digit and one for the tens digit, then adding them. Year 6 pupils should handle numbers up to four digits by two digits.
- 2,346 × 7 = 16,422First row: multiply by the 7 ones.
- 2,346 × 30 = 70,380Second row: multiply by 30. The placeholder zero shows we're multiplying tens.
- 16,422 + 70,380 = 86,802Add the two rows: 2,346 × 37.
Forgetting the placeholder zero in the second row is the classic error. It makes the answer roughly ten times too small, which a quick estimate (2,000 × 40 = 80,000) would catch immediately.
Short division
Short division (the “bus stop” method) divides by a single digit, carrying each remainder into the next digit. The common slip is forgetting to write a zero in the answer when a digit can't be divided: 816 ÷ 4 = 204, not 24.
Long division
Long division writes out each subtraction step and is used for dividing by two-digit numbers. The method is the same as short division, just with the working visible. Writing out the first few multiples of the divisor before starting (for ÷ 15: 15, 30, 45, 60…) turns each step into a simple lookup and removes most of the difficulty.
Year 6 pupils also need to express remainders in different ways: as a whole-number remainder, a fraction or a decimal, depending on what the question asks. A remainder of 3 when dividing by 4 can be written r 3, ¾ or .75.
In the SATs
The arithmetic paper always includes long multiplication and long division questions, each worth two marks. If the answer is wrong but the method is correct, one mark can still be awarded, but only if the working is shown in the answer box. That's a strong reason to teach a clear layout. Multiplication and division also run through the reasoning papers in word problems, scaling and measurement.
Common mistakes
- Missing the placeholder zero in long multiplication.
- Adding the carried digit before multiplying.
- Missing zeros in the quotient: 816 ÷ 4 = 24.
- Losing track of the subtraction steps in long division.
- Moving the decimal point the wrong way when multiplying or dividing by 10, 100 or 1,000.
Teaching ideas
Estimate the size
Before any long calculation, children round both numbers and estimate. They write the estimate beside the working and compare at the end. The placeholder zero error disappears quickly when pupils see their answer is ten times too small.
Multiples first
For long division, make writing the first five or nine multiples of the divisor a routine first step. It's slower at the start but far more accurate.
Show your working
Practise SATs-style answer boxes with space for working. Explain the method mark explicitly, so pupils understand why neat working matters even when they're confident.
Times tables, little and often
Every long method relies on recall of multiplication facts to 12 × 12. A few minutes of daily practice protects all the bigger methods built on top.
Try it: five quick questions
SATs-style questions to use as a starter or a quick check. Tap to see each answer.
Calculate 0.45 × 100.
Show answer
45
Calculate 1,234 × 26.
Show answer
32,084
Calculate 2,436 ÷ 6.
Show answer
406
Calculate 7,296 ÷ 24.
Show answer
304
Write the answer to 39 ÷ 4 as a decimal.
Show answer
9.75
Free worksheets for this topic
Printable A4 PDFs with answers. Free to use in class or at home.
