Long Multiplication

Long Multiplication

Long Multiplication involves multiplying two larger numbers together. Use either the long multiplication method or the box, or grid, method: both will give the same answer. Other methods also work.

The Long Multiplication method.

Set out the two numbers in rows with the larger number on top.  With the smaller number, select the units digit and carry out a short multiplication on the larger number.

Repeat again, but using the tens digit from the smaller number, placing this calculation on the line below: this is a multiple of 10, so start the short multiplication one digit to the left (set the units digit to zero).

If necessary, repeat for the hundreds digit, placing zeroes in the units and tens columns before doing the multiplication.

Finally, add the results of all the multiplications together.

The Grid, or Box, Method.

The Grid Method, or Box Method, works by multiplying every digit of one number against every digit of the other, taking into account the full value of both digits. After the multiplication is complete, the results of each multiplication are added together.

Example 1

Multiply 695 x 43 (using the long multiplication method).

Using the Long Multiplication method:

695 x 3 = 2085 and

695 x 4 x 10 = 27800 then add 2085 + 27800 = 29885

 3 2 2 1 6 9 5 x 4 3 2 0 8 5 2 7 8 0 0 2 9 8 8 5

Example 2

Multiply 695 x 43 (using the box/grid method).

695 is 600 + 90 + 5. 43 is 40 + 3

Multiply each combination of the numbers together

When the grid has been completed, add the columns, then add the column totals :

 x 600 90 5 40 24 000 3 600 200 25 800 3 1 800 270 15 3 870 25 800 3 870 215 215 29 885