Multiplication Tricks

There are a lot of tricks to multiply numbers in your head more quickly - read on to discover a few!

Multiply by 9: Use your hands! To multiply 7 by 9 hold your hands in front of you and bend your seventh finger (that`s the index finger on your right hand). Count the number of fingers you still have up, there are 6 to the left of your index finger and 3 to the right of it. Combining these numbers gives 63 = 7 x 9.

You can do any number up to 10 this way! The reason this works is that the leftmost digits in the 9 times tables increase like 0 1 2 3 ... while the right digits decrease like 9 8 7 6 ... So to get, for example 3 x 9 we get the left digit by counting out the third number on each list, that is 2 and 7 or 3 x 9 = 27.

Multiply by 11:

For small numbers you just double the digits - 4 x 11 = 44. For larger ones add the two digits and put the sum in between. For example what is 52 x 11?

5 + 2 = 7

therefore

52 x 11 = 572

If the sum is more than 9 you have to carry the 1.

39 x 11 = ?

3 + 9 = 12

therefore

39 x 11 = (3+1)29 = 429

You can see why this works by writing out the multiplication long hand

39 x 11 ______ 39 + 390 ______ 429

Multiply from left to right:

You read from left to right so why multiply from right to left? This way of multiplying is nice because you get the most important digits first, if you get good at doing this in your head you can just start saying the answer as fast as you could type the problem into a calculator!

For simple numbers it`s easy:

123123 x 3 = 369369

We just multiply each digit from left to right by 3. Because we don`t have to carry anything it works out okay. What about

628128 x 3 ?

This time as we multiply we write the extra tens digit above the ones digit and then add

1 2 2 628328 x 3 = 864964 __________ 1884984

In this example when we had 3 x 8 = 24 we carried the 2. For the first digit we had 3 x 6 = 18. There is nothing to add the tens digit to when we do the first multiplication so we can write it down from the beginning from now on.

Finally the most difficult example

644 49671 x 7 = 283297 __________- 347697 The tricky part here was when we had the 6+8=14. To take care of cases like these we have to look ahead one place when we are doing the addition. Before we write down the 2 we look ahead one place and see the next sum is going to give us a one to carry.

There are a couple of things to notice. The biggest sum we can make from two digits is 9 + 9 = 18. Because of this fact we will never have to carry more than 1. Also notice that the biggest product we can make is 9 x 9 = 81, that means the biggest number we have to put in the top row is 8. Even if there is a carry this brings us up to 9 and the biggest sum is still 9+9=18. Together this means we only ever have to look ahead one place! We never get a cascade of carries from left to right.

If you learn to do this in your head you should try holding the product of the next two numbers in your head. In the example above remember 4x7=28 and 9x7=63 add the first digit, 6, to 28 to give 34. You can continue in this way until you have the whole sum and best of all you start by getting the most important digits first so you can write down the answer, from left to right, as you calculate it!