Multiplication by 5

Most of us, especially those who know only the conventional right to left method of multiplication would pick choice a: 132,231 x 5. This is because the multiplier is composed of small digits.

But if you have read our Math Tip last week, we mentioned that mastering halving or dividing by 2 will help us multiply by 5 and later by 25 and 125. And halving, combined with doubling, can greatly expand our multiplication tables.

Moreover, our technique for halving numbers with odd digits, which we will also explain here, can be generalized as “short multiplication”.

As we wrote in our book 25 Math short Cuts, “To multiply a number by 5, move the decimal point 1 place to the right and halve it. If the number is a whole number, simply add a zero at the end of the number before halving it.” (You can order your copy of the book at the MATH-Inic Philippines FB page)

All the digits of choice b: 864, 648, are even and we can easily halve each digit starting from the left before we add a zero at the end. We will get the result 432 324 0. We can then adjust the placement of the thousand’s comma separator.

If want to announce the answer, we must first note the number to be multiplied by 5 is more than 8 hundred thousand. Therefore, the product must be in the millions. The mental process will be as follows:

            Half of 8 is four million          

            Half of 6 is three hundred

            Half of 4 is twenty

            Half of 6 is three thousand,

            Half of 4 is two hunded

            Halfof 8(0) is forty.

For choice b, because it contains some odd digits, there are additional steps. But those steps can help us learn “short multiplication”.

132, 231  is less than 200 thousand so multiplying it by 5 will result also in the hundred thousands. We will start to halve 13 instead of 1 as in conventional division.

Here are the mental steps:

            Half of 13 is six hundred (remainder 1 which we will place in front of the next digit 2)

             Half of 12 is sixty

            Half of 2 is one thousand,

            Half of 3 is one hundred (remainder 1 which we will prefix the next digit 1)

            Half of 11 is fifty (remainder 1. Which will become 10 when we add an ending zero)

            Half of 10 is five.     

More of “short division” in our succeeding posts.

Here are some practice exercises:

1. 64 x 5 =
2. 83 x 5 =
3. 284 x 5 =
4. 348 x 5 =
5. 4268 x 5 =
6. 1234 x 5 =
7. 32, 456 x 5 =
8. 75, 678 x 5 =
9. 243, 556 x 5 =
10. 975, 531 x 5 =

Here are the answers to last week’s exercises:

1. 248 ÷ 2 = 124
2. 628 ÷ 2 = 314
3. 4260 ÷ 2 = 2130
4. 6480 ÷ 2 = 4280
5. 2450 ÷ 2 = 1225
6. 3670 ÷ 2 =1835
7. 43,678 ÷ 2 = 21, 839
8. 34,786 ÷ 2 = 17, 393
9. 563, 458 ÷ 2 = 281, 729
10. 752, 356 ÷ 2 = 376, 178

If you are enjoying our Vedic Math Tips, we are inviting you to join the National and International Vedic Math competitions this year. See the schedule of Vedic Math activities here: https://www.math-inic.com/blog/revised-schedule-of-vedic-math-activities-in-the-philippines/

We are also conducting review webinars based on the questions used in last year’s Vedic Math Olympiads. Details are posted in our FB pages.