multiplying by 2 | The MSC Advantage

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


   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.

Discover the 25 Math Short Cuts ( 25 MSC )!

By Ike Prudente

This collection of 25 Math Short Cuts is published in commemoration of the 25th Foundation Day of MSC Institute of Technology.

I have selected what I think will be most useful for everyone, whether you are students, teachers, professionals or plain folks who need to calculate every day. Much of the hard work in compiling this work is not in researching for materials because I know these short cuts by heart but in selecting what short cuts to include.

From our grade school years, many of us have learned many ways of simplifying calculations. I am sure that for most of us, “multiplying by 10” is one of the first math short cut we have learned. And we continue to use it, which is the reason why I did not include it here. Unfortunately, most of us have forgotten most of the short cuts we have been taught in the past. As for my case, I am somewhat “lazy” at calculations so that I always looked for easier ways of computing. From my grade four teacher, I learned “squaring numbers ending in 5’ To this was added some more techniques which I picked-up from various books. I developed more short cuts by applying what I learned in algebra to simplify arithmetic computations. Then there were also some “tricks” I learned when I began to study “Vedic Math” in 2003, when they became available in the Internet.

$Math Short Cuts$

Even very young children can learn math short cuts, even adding left-to-right ( versus the traditional right to left )

I observed that my students enjoyed the short cuts that I shared with them and many came to love Math and actually improved their grades in the subject. I am also sure that these short cuts helped countless of my students pass the Philippine Science High School, UP Rural High School and UP entrance examinations.

Realizing that most readers like me, don’t want to read explanations, I will try to present the techniques in the form of examples, avoiding long explanations as much as possible. But sometimes we will cite Sutras or “word formulas” used in Vedic Math, which are very useful in remembering the short cuts.

We hope that with these shortcuts you will eventually be able to do most calculations mentally. However, we also realize that many will have to write down the answer first before reciting it. So we will explain the procedures to arrive at a written answer using a mental solution. With a little practice, many can dispense with the written answer.

Math Short Cuts (MSC)

We will add one short cut every week until Foundation Day 2014

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Math Short Cuts (MSC)

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