# Box Multiplication Method (Multiplying TU Times Tu).

If you are multiplying two large numbers (TU by TU) then the box multiplication method is probably one of the easiest methods to use.

All you need is a 3 by 3 table. Split your first number into tens and unit and write this across the top of the table.  Also split the second number into tens units and write this down the side of the table. Next, work out the numbers that go into the remaining four spaces. For each of the four missing boxes, multiply the number at the top of the box by the number at the side of the box. Once you have worked these out, add up these four numbers to give the final answer.

Let’s go through a couple of examples of box multiplication.

Example 1

Work out 18 × 46.

Partitioning 18 gives 10 and 8, write these across the top of the table.

Partitioning 46 gives 40 and 6, write these down the side of the table.

Next, work out the numbers that go into the four missing boxes by multiplying the numbers at the top by the numbers at the side. A good way to do this is to ignore the zeros at the end of each number and add them onto the end of your answers.

10 × 40 gives 400

8 × 40 gives 320

10 × 6 gives 60

8 × 6 gives 48

Now all you need to do now is add these numbers up.

400 + 320 + 60 + 48 = 828

Example 2

Work out 73 × 64.

Partitioning 73 gives 70 and 3, write these across the top of the table.

Partitioning 64 gives 60 and 4, write these down the side of the table.

As in the last example, work out the numbers that go into the four missing boxes by multiplying the numbers at the top by the numbers at the side.

70 × 60 gives 4200

3 × 60 gives 180

70 × 4 gives 280

3 × 4 gives 12

Now all you need to do now is add these numbers up.

4200 + 180 + 280 + 12 = 4672

Extra Help

Grid multiplying

Box multiplication TU by U, HTU by U

Box multiplication HTU by TU