Next easiest after multiplication by 11, is multiplication by 2. Multiplying a number by 2 is also called doubling. Doubling may be done by adding a number to itself but it is easier to apply the “times two” table that we have learned by heart.
Let us call 0, 1, 2, 3 and 4 “small digits” and 5, 6, 7, 8 and 9 “ big digits”. I am sure that there will be no problem in doubling the small digits into 0, 2, 4, 6 and 8 respectively.
Note that if we subtract 5 from a big digit, we will get a small digit. i.e.
 big digit 5 minus 5 = small digit 0.
 big digit 6 minus 5 = small digit 1.
 big digit 7 minus 5 = small digit 2.
 big digit 8 minus 5 = small digit 3.
 big digit 9 minus 5 = small digit 4.
With small digits, doubling is very easy: From the left, we simply double each digit and write the answer below it.
Example 5.1:
2 4 3 1
x 2
4 8 6 2
With big digits, we modify our procedure: Double each digit starting from the left, but before we write our answer, look at the next digit to the right, if it is “big” add 1 to it. Deduct 5 from the next digit,before doubling it.
Example 5.2:
4 8
x 2
9

4 8
x 2
9 6

Doubling 4 gives 8 it before putting it down, we note that the next digit to be doubled is 8 which is big, so we add 1 first to make it 9. We then deduct 5 from 8 to make it 3 before doubling to get 6.
An important skill that can be developed by first practicing on doubling is distributed multiplication.
Example 5.3:
4 8
x 2

4 0 +
x 2
8 0 +

8
x 2
1 6 = 9 6

Or
4 8
x 2

4 5 +
x 2
9 0 +

3
x 2
6 = 9 6

Longer numbers can be split.
Example 5.4:
3 8 4 6
x 2

3 8  4 6
x 2  x 2
7 6  9 2

3 8 4 6
x 2
7 6 9 2

Exercise 5.1: Double the following numbers
 2,3 4 3
 2,5 3 5
 4,5 2 7
 3,5 5 2
 5,5 5 5
 8,4 7 7
 6,3 8 6
 3,0 9 9
 3,9 0 9
 7,8 9 6
To multiply by 4, we can double two times.
Example 5.5: 237 x 4=
 237 x 2 = 474
 474 x 2 = 948
To multiply by 8, we can double three times.
Example 5.6: 632 x 8 =
 632 x 2 = 1,264
 1,264 x 2 = 2,528
 2,528 x 2 = 5,056
Exercise 5.2: Find the following products:
 142 x 4 =
 357 x 4 =
 568 x 4 =
 742 x 4 =
 2468 x 4 =
 214 x 8 =
 455 x 8 =
 773 x 8 =
 894 x 8 =
 3152 x 8 =
Answers to all exercises are found in the answer key.
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