Multiplying large numbers
Now, let’s look at multiplication.
How would we go about multiplying 262 by 397?
We want to calculate 262 * 397.
When we multiply large numbers by hand (without a calculator) it is helpful to write one number on top of the other with the ones, tens, hundreds etc. lined up, like this:
Now, this calculations could be written as
2 * 394
+ 60 * 394
+ 200 * 394
or
2 ones x 394
+ 6 tens x 394
+ 2 hundreds x 394
We do the multiplication by starting with 2 ones multiplied by 394
We multiply the 2 by the ones in 394. There are 4 ones
Then we multiply the 2 by the tens in 394. There are 9 tens.
We need to carry the one. This means move the 1 from 18 over into the column to the left. This is because 18 tens are the same as 1 hundred and 8 tens.
Then we multiply the two by the three hundreds. We need to remember to add the one hundred we have carried over from the tens column.
We have finished the first part of our multiplication, now we need to do the second part.
2 ones x 394
+ 6 tens x 394
+ 2 hundreds x 394
We are going to multiply the 6 tens in 262 by 394 and add the result below the 788 we have just calculated.
First we add a 0 in the ones column. This is because we are multiplying 6 tens. If we add the 0 in the ones column then we are taking account of the tens and we can multiply 394 by 6 instead of 60.
We multiply the 6 in 262 by 394 starting with the ones column. 6 * 4 = 24. We carry the 2.
Next we multiply by the tens and remember to add the 2 we have carried.
We carry the 5 in 56.
Finally, we multiply 6 by the 3 hundreds in 394. Again we need to add the number carried from the previous calculation.
We write the 23 in our answer line.
We have finished the second part of our multiplication, now we need to do the third and final part.
2 ones x 394
+ 6 tens x 394
+ 2 hundreds x 394
This time we will be multiplying the 2 hundreds in 262. Two hundred is written as 200. We can add to two 0s to our answer line and then multiply by 394 by 2 because we have taken the hunderds into account.
This time we will be multiplying the 2 hundreds in 262. Two hundred is written as 200. We can add to two 0s to our answer line and then multiply by 394 by 2 because we have taken the hunderds into account.
Now we will multiply the first 2 in 262 by 394. We already know from multiplying the last 2 in 262 by 394 that 2 x 394 = 788 so we can write the 788 on the answer line.
Now we have completed the three parts in our multiplication
2 ones x 394
+ 6 tens x 394
+ 2 hundreds x 394
This is 788 + 23640 + 78800
We add these numbers together in the way of adding any large numbers.
First the ones column.
Then the tens. Remember to carry the one.
Then the hundreds. Remember to add the one and there is a two to carry this time.
Carry on in this way…
When we complete the addition we find that 262 * 394 = 103228
