Now we multiply crossways: 3 × 6 and 7 × 4, and then multiply the answer by 10.
3 × 6 = 18
7 × 4 = 28
18 + 28 = 46
46 × 10 = 460
Our subtotal was 2,100. To this we add 400, then we add 60.
2,100 + 400 = 2,500
2,500 + 60 = 2,560
We are nearly there. Now we multiply the units digits, and add.
4 × 6 = 24
2,560 + 24 = 2,584
Try doing the problem yourself in your head. You will find it is easier than you think. Calculating
from left to right means there are no numbers to carry.
The calculation is not as difficult as it appears, but your friends will be very impressed. You just need
to practice shrugging your shoulders and saying, ‘Oh, it was nothing.’
If you can’t find an easy way to solve a problem using a reference number then direct multiplication
might be your best option.
Direct multiplication using negative numbers
I debated with myself whether this section should be included in the book. If you find it difficult, don’t
worry about it. Try it anyway. But you may find this quite easy. It involves using positive and negative
numbers to solve problems in direct multiplication. If you try it and you think it is too difficult, forget it
— or come back to it in a year’s time and try it again. I enjoy playing with this method. See what you
think. Here is how it works.
If you are multiplying a number by 79 it may be easier to use 80 − 1 as your multiplier. Multiplying
by 79 means you are multiplying by two high numbers and you are likely to have high subtotals.
Multiplication by 80 − 1 might be easier. Using 80 − 1, 8 becomes the tens digit and −1 is the units
digit. You need to be confident with negative numbers to try this.
Let’s have a go:
68 × 79 =
We set it out as:
We begin by multiplying the units digits. Eight times minus 1 is minus 8. We don’t write −8; we
borrow 10 from the tens column and write 2, which is left over when we minus the 8. We carry −1 (ten),
which we borrowed, to the tens column.
The work looks like this:
Now we multiply crossways. Eight times 8 is 64, and 6 times −1 is −6.
64 − 6 = 58
We subtract the 1 that was carried (because it was −1) to get 57. We write the 7 and carry the 5.