Lets take an example
We'll take 7 x 8
Write 7 x 8 "" down on a piece of paper and draw a circle below each number to be multiplied.
7 x 8 =
O O
Now go to the first number to be multiplied, 7. How many more do you need to make l0. The answer is 3. Write 3 in the circle below the 7. Now go to the 8. What do we write in the circle below the 8? How
many more to make 10? The answer is 2. Write 2 in the circle below the 8.
Your work should look like this:
7 x 8 =
O3 O2
Now subtract diagonally. Take either one of me circled numbers (3 or 2) away from the number, nO[ directly above, but diagonally above, or crossways. In other words, you either take 3 from 8 or 2 from 7. You only subtract one time, so choose the subtraction you fmd easier. Either way, the answer is the same, 5. This is the first digit of your answer.
8-3 = 5 or 7 - 2 = 5
Now multiply the numbers in the circles. Three times 2 is 6. This is the last digit of your answer. The answer is 56. This is how the completed problem looks.
7 x 8 = 56
O3 O2
If you know the 2 times tables reasonably well, you can easily master the rabies up to the 10 times table, and beyond. Let's try another example, 8 x 9.
8 x 9 =
O2 O1
How many more to make to? The answer is 2 and 1. We write 2 and1 in the circles below the numbers. What do we do now? We subtract diagonally.
8-1 =7 0r 9-2 =7
Seven is the first digit of your answer. Write it down. Now multiply the two circled numbers.
2x1=2Two is the last digit of [he answer. The answer is 72.
Isn't that easy? Here are some problems to try by yourself. Instead of
writing the answers in the book, you may prefer to write the answers
on a piece of paper or in a notebook so that you can do the problems
again if you wish .
Multiplication by Factors
IT is easy to multiply by 20, as ZO is 2 times to. And it is simple to multiply by 10 and by 2. This is called multiplication by factors, as 10
and Z are factors of 20.
10 x 2 = 20
Let's try an example:
23 x 24 =
Twenty~three and 24 are higher than the reference number, 20, so we put the circles above. How much higher are they? Three and 4. We
write these numbers in the circles. We write them above because they are plus numbers
(23 - 20 + 3, 24: 20 + 4) .
O3 O4
23 x 24 =
We add diagonally as before:
23 + 4 = 27 or,
24 + 3 = 27
Now multiply this answer, 27, by the reference number 20. To do this we multiply by 2, then by 10:
27 x 2 = 54
54 x 10 = 540
(Later, in this chapter, will look at an easy way to multiply numbers like 27 by 2.) The rest is the same as before. We multiply the numbers
in the circles and add this to our subtotal:
3 x 4 = 12
540 + 12 = 552
Your work should look like {his:
O3 O4
23 x 24 = 27
540
+12
552 ANSWER
Checking Our Answers
Let's apply what we learned in Chapter Four and check our answer:
23 x 24 = 552
5 6 12
3
The substitute numbers for 23 and 24 are 5 and 6.
5 x 6 = 30
3 + 0 = 3
Three is our check answer.
The digits in our original answer, 552, add up w 3:
5 + 5 + 2 = 12
1 + 2 = 3
This is the same as our check answer, so we were right.
