Multiplication II

We draw the circles below the numbers and subtract the numbers we are multiplying from 10. We write 4 and 3 in the circles. Our problem looks like this:

Now we subtract crossways: 3 from 6 or 4 from 7 is 3. We write 3 after the equals sign.

Four times 3 is 12, so we write 12 after the 3 for an answer of 312.

Is this the correct answer? No, obviously it isn’t.

answer

Let’s do the calculation again, this time using the reference number.


Th at’s more like it.

Test yourself

Try these problems using a reference number of 10:

a) 6 × 7 =

b) 7 × 5 =

c) 8 × 5 =

d) 8 × 4 =

e) 3 × 8 =

f) 6 × 5 =

The answers are:

a) 42                 b) 35             c) 40

d) 32                 e) 24             f) 30

What was our reference number for 96 × 97 in Chapter 1? One hundred, because we asked how many more do we need to make 100.

The problem worked out in full would look like this :

answer

Th e technique I explained for doing the calculations in your head actually makes you use this method. Let’s multiply 98 by 98 and you will see what I mean.

If you take 98 and 98 from 100 you get answers of 2 and 2. Then take 2 from 98, which gives an answer of 96. If you were saying the answer aloud, you would not say, “Ninety-six,” you would say, “Nine thousand, six hundred and . . .” Nine thousand, six hundred is the answer you get when you multiply 96 by the reference number, 100.

Now multiply the numbers in the circles: 2 times 2 is 4. You can now say the full answer: “Nine thousand, six hundred and four.” Without using the reference number we might have just written the 4 after 96.

Here is how the calculation looks written in full:

answer

Test yourself

Do these problems in your head:

a) 96 × 96 =

b) 97 × 97 =

c) 99 × 99 =

d) 95 × 95 =

e) 98 × 97 =

Your answers should be:

a) 9,216                        b) 9,409                         c) 9,801

d) 9,025                        e) 9,506