# Viral Math Hacks Videos

A Facebook video entitled “Become advanced in multiplication with these easy hacks” (Video | Facebook) has recently became viral with over 2.6 million plays.

It featured techniques in multiplying

- 31 x 51 and 31 x61
- 509 x 509
- 12, 23, 34, and 45 by 11
- and 75 x 75.

As with most “math hacks” posted in social media, the techniques work for the specific sets of figures presented but not in others. Sadly, most of these videos do not explain why those shortcuts work.

As shown in the video, in getting the product of 31 and 51, the units digit of the product is obtained by multiplying the unit’s digits of the multiplicands, 1 x 1 = 1.

The next step is to multiply the ten’s digits of the multiplicands to get the first two digits of the answer.

In the video the last step was to add 3 and 5 to get 8, the ten’s digit of the product.

The method used works well with the given figures, where the unit’s digits of multiplicands are both 1 and the sum of the ten’s digits is less than ten. But it will not give the correct answer for 32 x 51 or for 31 x 81.

The correct algorithm is the vertically and crosswise sutra which was the one used in multiplying 75 x 75, although there is an easier way to solve that particular problem.

The first step in the correct algorithm is the same as in the video except that 1 x 1 is expressed as 01.

The second step, 3 x 5 is really 30 x 50 but the two ending zeroes are not written.

The third step is actually (30 x 1) +(50 x 1) = 80

This procedure can be used for any 2-digit by 2-digit multiplication. The steps in this vertically and crosswise method may be interchanged but the result will be the same.

We will discuss the other hacks in future posts.

Try these multiplications:

- 32 x 41 =
- 31 x 42 =
- 33 x 51 =
- 31 x 53 =
- 61 x 23 =
- 41 x 61 =
- 31 x 81 =
- 42 x 52 =
- 53 x 23 =
- 72 x 23 =

Answers to exercises in the “Division by 9 with regrouping” article (Division by 9 with regrouping – MATH-Inic)

- 56 ÷ 9 = 6 r 2
- 86 ÷ 9 = 9 r 5
- 467 ÷ 9 = 51 r 8
- 582 ÷ 9 = 64 r 6
- 4732 ÷ 9 = 525 r 7
- 7514 ÷ 9 = 834 r 8
- 38643 ÷ 9 = 4293 r 6
- 55455 ÷ 9 = 6161 r 6
- 662772 ÷ 9 = 73641 r 3
- 283746 ÷ 9 = 31527 r 3