Calculation methods for multiplication

For simple multiplication, you can memorize the multiplication tables. Or you can count in your head. Five times four equals 20. But how do we multiply larger numbers such as 428 times four? 428 is not in the multiplication tables.

One method that you could use, is to divide the number into different place values. Hundreds, tens and ones. This method is called decomposing numbers. 428 is then divided into 400, 20 and eight. Multiply each of the place values individually by four.

400 times four is 1600. 20 times four is 80. Eight times four is 32. Add the results together. 1600 plus 80 plus 32 is..

1712. Here we have Leonardo Fibonacci. In the 13th century he published a book on mathematics describing a multiplication method that was common in India. We will use this method on the previous calculation, 428 times four. Draw a square for each of the digits in the largest number, 428.

Write four above the first box, two above the second and eight above the third. Write the second number, four, to the right of the boxes. Draw a line from the top right corner to the bottom left corner in each box. Begin multiplying the individual numbers from the right. Eight times four is 32.

Write the tens, three, in the upper part of the box and the ones, two, in the lower part of the box. Next digit. Two times four is eight. Zero in the tens part of the box and eight in the ones part of the box. Four times four is 16.

One ten and six ones. Following the numbers on an angle, we add the digits in each oblique box. The first “oblique box”, only has one number, two. Copy the two under the box. In the next oblique box there is a three and an eight.

Add them to make 11. Write one under the second box and a small one, for the tens, as a memory digit under the next box to the left. In the next oblique box add zero plus six, plus the memory digit, one. That equals seven. Cross out the used memory digit.

The last, “oblique box” has only the number one. Copy ‘one’ to the left of the first box. The answer of 428 times four is 1712. This is called the gelosia method because the method looks like the iron grids, jalousie, they had covering the windows in Leonardo Fibonacci’s time. Goodbye Leonardo!

A third method is to write the numbers on top of each other. Hundreds in a column tens in a column, and ones in a column. The method is called stacking. Here we will try 428 times 24. Place the larger number, 428 above the smaller number, 24.

Multiply the four in 24 by each of the digits in 428. Four times eight is 32. Write two under the line and a small three next to 24 to carry it over to the next multiplication. Four times two is eight, and then we add the digit we carried over, three, for a total of 11. Write ‘one’ under the line and a ‘one’ to carry over to the next multiplication.

Cross out the three so we know it is used. Four times four is 16. Add the digit we carried over,‘one’, for a total of 17. Write 17 below the line. Cross out the number we carried over.

Now we multiply using the next digit in the number 24, the two. Two times eight is 16. Since the two in the number 24 is actually two tens, we write the six under the tens column in 1712, under the ‘one’. The ‘One’ from the 16 is carried over. Two times two is four.

Add the ‘one’ we carried over for a total of five. Cross out the number we carried over. Multiply two by four. That is eight. Write eight.

Then we add the results together in each column. Two plus nothing, or zero, is two. One plus six is seven. Seven plus five is 12. Write two under the line and carry over the ‘one’ to the next column.

One plus eight is nine. Add the ‘one’ we carried over for a total of ten. Write 10 under the line. Answer: 428 times 24 is 10272. There are many more methods for multiplying large numbers.

It is important that you find one that you feel comfortable with and understand.