Year 5 maths · Key Stage 2 · Number – multiplication and division

Year 5 long multiplication and short division: a guide

In Year 5 children move on from short multiplication to long multiplication, multiplying a number of up to four digits by a two-digit number on paper. They divide up to four digits by one digit using short division and decide what to do with a remainder. They also multiply and divide whole numbers and decimals by 10, 100 and 1,000, calculate mentally from facts they already know, and use the equals sign correctly in multi-step problems.

Long multiplication and short division, explained

Long multiplication is used when both numbers have more than one digit, such as 346 × 24. The calculation is split into two easier ones: 346 × 4 and 346 × 20. Each gets its own row and the two rows are added together. The second row starts with a zero in the ones column, a placeholder, because multiplying by 20 is multiplying by 2 and then by 10, and multiplying by 10 moves every digit one place to the left. This is the distributive law, which the curriculum guidance writes as a(b + c) = ab + ac: 346 × 24 is the same as 346 × 20 + 346 × 4. Many schools first teach it as a grid, with the number partitioned and each part multiplied separately, before moving to the column layout. Both are the same arithmetic written differently.

Short division, sometimes called the bus stop method, shares a number of up to four digits by a single digit, working from the left. For 98 ÷ 4, 9 tens shared into 4 groups gives 2 tens in each group with 1 ten left over. That ten is exchanged for 10 ones and joins the 8 ones to make 18, and 18 ÷ 4 is 4 with 2 left over. The answer is 24 remainder 2. The same steps work for bigger numbers, such as 4,735 ÷ 6 = 789 remainder 1. Long division, with a two-digit divisor, is not expected until Year 6.

A remainder is only the start of the answer. Teachers show the same calculation, 98 ÷ 4, answered several ways: 24 remainder 2, 24 and a half, 24.5, or about 25, depending on the question. Sharing 98 sweets between 4 children leaves 2 sweets over. Sharing £98 between 4 gives £24.50 each. Carrying 98 people in cars that each hold 4 needs 25 cars, because the last two people still need a lift. Children are asked to read the context and decide whether to round up, round down, or write the leftover as a fraction or decimal.

Multiplying and dividing by 10, 100 and 1,000 is about place value, not about adding or removing zeros. Each digit moves one, two or three places to the left when multiplying, and to the right when dividing, so 3.4 × 100 = 340 and 45 ÷ 1,000 = 0.045. This is the idea behind changing between kilometres and metres or centimetres and metres, and behind scale drawings. Children are also expected to use known facts: because 6 × 7 = 42, they should be able to say that 60 × 7 = 420 and that 4,200 ÷ 6 = 700.

Written methods sit alongside problem solving. Year 5 questions combine all four operations, include simple rates (“5 pens cost £3.50, so what do 8 cost?”) and scaling by simple fractions (“a ribbon one third as long as 24 cm”). The equals sign is taught as meaning “has the same value as”, so children should be comfortable with statements such as 13 + 24 = 12 + 25, where both sides come to 37. Long multiplication and short division both appear in the arithmetic paper of the Key Stage 2 tests in May of Year 6, so Year 5 is the time to make them secure.

Words your child will hear

Long multiplication: A written method for multiplying by a number with two or more digits, using one row for each digit of the multiplier.
Short division: A written method that divides by a one-digit number, working from the left and exchanging anything left over into the next place to the right.
Remainder: What is left over when a number doesn’t divide exactly. 98 ÷ 4 leaves a remainder of 2.
Placeholder: A zero that holds a place so the other digits stay in the right columns, as in the second row of long multiplication.
Product: The answer to a multiplication. The product of 346 and 24 is 8,304.
Inverse: The opposite operation. Multiplication checks division, so 24 × 4 + 2 = 98.
Equals sign: The symbol = means “has the same value as”, not “the answer comes next”.

What the National Curriculum says

In Year 5, pupils should be taught to:

Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
Multiply and divide numbers mentally, drawing upon known facts
Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
Multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Work out 346 × 24 using long multiplication.

Estimate first. 346 is close to 350, and 350 × 24 = 7,000 + 1,400 = 8,400. The answer should be a little under 8,400.
Write the numbers in columns with the ones lined up. Multiply 346 by the 4 ones: 4 × 6 = 24, so write 4 and exchange 2 tens. Then 4 × 4 = 16 tens, plus the 2 makes 18, so write 8 and exchange 1 hundred. Then 4 × 3 = 12 hundreds, plus 1 makes 13 hundreds. The first row is 1,384.
```
      3 4 6
    ×   2 4
    -------
    1 3 8 4   346 × 4
```
Now multiply by the 2 tens, which is really 20. Write a zero in the ones column as a placeholder. Then 346 × 2 = 692, written to the left of the zero. The second row is 6,920.
```
      3 4 6
    ×   2 4
    -------
    1 3 8 4   346 × 4
  + 6 9 2 0   346 × 20
```
Add the two rows, starting with the ones: 4 + 0 = 4, 8 + 2 = 10, 3 + 9 + 1 = 13 and 1 + 6 + 1 = 8.
```
    1 3 8 4
  + 6 9 2 0
    -------
    8 3 0 4
```
Compare with the estimate. 8,304 is a little under 8,400, so the answer is sensible.

346 × 24 = 8,304

Common mistakes and how to help

Leaving out the placeholder zero in the second row

The second row is multiplied correctly, but it is written starting in the ones column. That makes 346 × 24 come out at 1,384 + 692 = 2,076, far too small.

What helps: Estimate first and compare. Remind your child that the second row is “times 20”, so its ones column can only hold the placeholder zero. A grid of 300, 40 and 6 times 20 and 4 shows where every part goes.

Giving a remainder when the question needs something else

A child divides 98 by 4, writes 24 r 2 and stops. Division is often practised without a context, so the answer to the calculation becomes the answer to the question.

What helps: Reread the question and ask what the leftover means. For people travelling in cars of 4, 24 cars leaves 2 people stranded, so 25 are needed. For money, the leftover becomes a decimal.

“To multiply by 10, add a zero” with decimals

The shortcut works for whole numbers, so children apply it to 3.5 × 10 and write 3.50. Writing a zero on the end of a decimal doesn’t change its value.

What helps: Describe it as every digit moving one place to the left: the 3 ones become 3 tens and the 5 tenths become 5 ones, so 35. Check with a measure: 3.5 cm is 35 mm, not 3.50 mm.

Reading the equals sign as “now write the answer”

For years the sign has appeared in 3 + 4 = 7, so a child sees 13 + 24 = 12 + ? and fills in 37, or writes chains such as 13 + 24 = 37 + 5 = 42.

What helps: Talk about a balance: both sides must weigh the same. Ask “what is each side worth?” before filling the gap, and write one calculation per line.

How to help at home

Estimate before you work it out. Before any calculation, ask for a rough answer by rounding: “346 × 24 is a bit less than 350 × 24. What is that?” Estimating is the quickest way to catch a missing placeholder or a missed exchange.
Make remainders real. Use everyday problems and let your child decide what the leftover means: 38 people and cars that hold 5, or £50 shared between 4. The same calculation can need rounding up, rounding down or a decimal.
Move digits with a metre stick or scales. Ask how many millimetres are in 3.4 m, or how many grams are in 2.5 kg, and talk about how each digit moves. Kitchen scales and a tape measure give instant checks.
Price and rate puzzles. “Three apples cost £1.20. What do seven cost?” Finding the price of one first (40p), then scaling up, is exactly the rate thinking used in Year 5 problems.
Balance the equals sign. Write 6 × 8 = 4 × ? or 15 + 27 = 20 + ? and ask your child to explain how they know the missing number keeps the sides equal. Making up their own for you to solve works well too.

Builds on

Year 4: Times tables to 12 × 12

Leads on to

Year 6: Long multiplication and division
Year 6: Order of operations and multi-step problems