Long multiplication explained for parents

What it is

Short multiplication

The written method for multiplying by a one-digit number, such as 124 × 6, all on one line.

Long multiplication

The written method for multiplying by a two-digit number. It needs two rows of working, then an addition.

Partial products

The answers to each part of the calculation. In 124 × 26, they are 124 × 6 and 124 × 20.

Place holder

The 0 written in the ones column of the second row, because that row is multiplying by tens.

Long multiplication rests on one simple idea: 26 is 20 + 6. So 124 × 26 is the same as 124 × 6 added to 124 × 20. The written layout just keeps those two parts tidy.

124 × 6  =   744
124 × 20 = 2,480
744 + 2,480
         = 3,224

Your child needs their times tables to do this. DfE guidance for teachers points out that the facts up to 9 × 9 are the ones written multiplication depends on.

How it's taught at school

Written multiplication builds up over a few years. In Year 3, children start writing out two-digit times one-digit calculations. In Year 4, they learn to split a number into parts to multiply, such as 14 × 3 as 10 × 3 add 4 × 3, and they multiply two- and three-digit numbers by a one-digit number using a formal written layout, which is short multiplication.

In Year 5, the national curriculum adds long multiplication: children multiply numbers with up to 4 digits by a two-digit number. In Year 6, they keep using it and become fluent.

    1 2 4
  ×   2 6
  -------
    7 4 4
  2 4 8 0
  -------
  3 2 2 4

1. Multiply by the ones digit, 6. 4 × 6 = 24: write 4 in the ones column and regroup the 2 tens by writing a small 2 in the tens column. 2 × 6 = 12, plus the 2 regrouped tens makes 14: write 4 and regroup 1 hundred. 1 × 6 = 6, plus 1 makes 7. The first row is 744.
2. Multiply by the tens digit, 2, which is really 20. Write a 0 in the ones column first as a place holder. Then 4 × 2 = 8, 2 × 2 = 4, 1 × 2 = 2. The second row is 2,480.
3. Add the two rows. 744 + 2,480 = 3,224.
4. Check it is sensible. 124 is about 100 and 26 is about 30, so the answer should be roughly 3,000. 3,224 is close.

Schools differ in small ways. Some write the tens row first, and the small regrouped digits go in slightly different places. The national curriculum's own examples show both orders and say these details vary, so follow your child's school. DfE guidance calls this step regrouping, though you may know it as carrying.

Children are also taught to estimate before they calculate, and DfE guidance suggests they learn to check written multiplication with a calculator. They should choose between short and long multiplication too: 124 × 6 only needs one row.

Common mistakes (and how to help)

Forgetting the 0 place holder in the second row

Without it, 124 × 26 becomes 744 + 248 = 992, which is far too small. Go back to the estimate: about 3,000. Then ask "Is the 2 in 26 worth 2 or 20?"

Forgetting to add the regrouped digits

Without them, 124 × 6 comes out as 624 instead of 744. Encourage your child to write each regrouped digit small and clearly, and to cross it out once it's been used.

Mixing up the regrouped digits from the two rows

Regrouped digits from the first row can get added into the second by mistake. Crossing them out after use, or writing the second row's regrouped digits in a different spot, keeps them apart.

A slow or shaky times table fact throws the whole answer out

Long multiplication is lots of times table facts in a row, so one wrong fact gives a wrong answer. Short, regular practice of the facts up to 9 × 9 makes the method much smoother.

Three quick activities at home

Questions parents ask

Sources

1. Department for Education: National curriculum in England: mathematics programmes of study
2. Department for Education: Teaching mathematics in primary schools (Mathematics guidance: key stages 1 and 2)
3. BBC Bitesize: Long multiplication (KS2 Maths)