Easy Math Multiplication

Added Friday 03.07.2009

Maths, not for everybody, and easier for some than others. Whether you like mathematics or not it exists in our daily lives, the most common interaction with numbers being money. If you have trouble with multiplying numbers or just want to improve your multiplication ability to exclude the use of a calculator there are quite a few techniques to help you. You don't need to pay for these, I will show you some below, and of course there are many, many more.

Double Digit Multiplications in one step
This technique is very handy for working out any two digit multiplication quickly in one step (or one line) and can easily be done mentally.

First, take any two digit multiplication, for example:

12

x 34

Next, to get the smallest digit you simply multiply the last digits (right most) from each number, 2 and 4. So, 2 x 4 = 8. If the number is more than one digit, we will carry the extra digits to use later.

12

x 34

8

The middle section is slightly more involving. Take the first digit of the first number and multiply it with the second digit of the second number, then add it to the multiplication of the second digit of the first number with the first digit of the second number, ie. (1 x 4) + (2 x 3) = 10. If there was a carry from the first step just add this to the number, and again, if the result is more than one digit we will carry the extra digits. So, with the result of 10, the '0' becomes the next digit in the answer, and '1' (extra digit) is carried.

12

x 34

08

To get the final digits of the answer multiply the first digits (left most) of each number, plus adding any previous carry (in this example '1'). 1 x 3 = 3, plus carry, 3 + 1 = 4.

12

x 34

408

Try this for other numbers. Check with a calculator if you want!

89

x 76

First part of answer, 9 x 6 = 54. Use the 4, carry the 5.

89

x 76

4

Second part, (8 x 6) + (9 x 7) = 48 + 63 = 111, plus carry, 111 + 5 = 116. Use the 6, carry the eleven.

89

x 76

64

Last part, 8 x 7 = 56, plus carry, 56 + 11 = 67. Done!

89

x 76

6764

Triple Digit Multiplications in one step
To do triple digit multiplications we can use the two digit method and add a few more steps. See the video below for example.

Russian Peasant Multiplication
This technique essentially eliminates multiplication and only relies on adding, halving, and doubling, or adding, division by 2 and multiplication by 2. So you can use this technique if anything bigger than two times multiplication is troubling! Ok, how does it work?

First, start with the your two numbers, and place them in two columns. For example, 58 x 87 becomes:

58

87

Ok, now the rules. Writing down the page, you double first column, and halve the second column. If the second column gives a remainder just round down. Stop when the second columns becomes 1.

58 116 232 464 928 1856 3712

87 43 21 10 5 2 1

Now, cross out any rows where the second column is even. Then, add the total of the uncrossed lines in the first column:

58 116 232 464 928 1856 3712	87 43 21 10 5 2 1
5046

And there we go, 58 x 87 = 5046.

Crossing Lines Multiplication
This technique is very basic and can apply to almost any multiplication. It involves drawing lines and counting intersections, no multiplication, halving, doubling, just counting and simple adding. Even though the principle is very simple very large numbers can create quite a mess of lines making it impossible without a ruler and no longer becoming practical.

Other techniques
These are just a taster of some of the techniques. Feel free to post comments or other methods. If you strongly recommend any other techniques please email and I will be happy to post them so everybody else can share for free!

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