Multiplying by 11

Do you know that multiplying by 11 is easier than multiplying by 2?

That is the reason that in my best-selling book 25 Math Short Cuts, I discussed multiplication by 11 in Chapter 4, ahead of multiplication by 2 which is tackled in Chapter 5. (25 Maths Short Cuts is available in printed and e-book versions. Send message to MATH-Inic Philippines to order.)

When I was just starting MATH-Inic, I had an opportunity to demonstrate Vedic Math to grade six students. In one of the lower sections, when the learners were told that I will discuss Math, many of them started transferring to the back rows. Some even asked permission to go out.

But when I explained to them the “buka” method of multiplying by 11, I saw many of them smiling and many started to go back to their seats in front. In just a short time, I managed to show them that MATH can be “fun, fast and easy”. And as the session went on, most of them enjoyed calculating mentally.

What exactly is the “buka” method?

In multiplying a two-digit number by 11, we just 1) separate (‘ibuka”) the digits and 2a) insert their sum in between them if it is less than 10 else 2b) add 1 to the first digit and insert the unit’s digit between the original digits.

This technique is very easy to learn and I consider it one of the best way to develop interest in Math. If there are no regrouping or “carries” this technique is very easy even will longer multipliers.

In our example 815427 x 11, we can immediately give the answer digit by digit. If we want include the place values in the answer, we must first note that since the multiplier has 6 digits the answer must be in the millions. Thus 815,427 x 11 is

eight million

8 + 1 = nine hundred

1 + 5 = sixty

5 + 4 = nine thousand

4 + 2 = six hundred

2 + 7 = ninety

seven

We will discuss multiplication by 11 with “carries” next week

Exercises: Multiply mentally

1. 23 x 11 =
2. 63 x 11 =
3. 234 x 11 =
4. 725 x 11 =
5. 5261 x 11=
6. 7163 x 11 =
7. 52361 x 11 =
8. 71635 x 11=
9. 8080808 x 11 =
10. 12121212121 x 11 =

Here are the answers to last week’s exercises

1. 280 ÷ 5 = 56
2. 670 ÷ 5 =134
3. 325 ÷ 5 = 65
4. 745 ÷ 5 = 149
5. 1230 ÷ 5 = 246
6. 5670 ÷ 5 = 1134
7. 2345 ÷ 5 = 469
8. 8345 ÷ 5 = 1669
9. 18340 ÷ 5 = 3668
10. 23635 ÷ 5 = 4727