How can you multiply 2-digit numbers using mental math?

Answer 1

There are several methods for doing this, but first, you should already be comfortable with adding 2 and 3 digit numbers. Practice this if you don't have confidence in your skill.

In any of these methods, it helps to view the numbers on a grid, starting with the given two numbers each on their own line, just like when doing hand calculations. In the following examples, 'o' is used instead of '0' to represent "floating" numbers, i.e. numbers that have been shifted to the left by a certain number of spaces. The 'o's don't have to be a part of your mental image.

Now as an example, try to multiply these two numbers:

53

29

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If you are comfortable multiplying two-digit numbers by one-digit numbers, then you could do it "textbook style": multiply the first number by the tens and then the ones (or vice verse) of the second number, and add the two results:

__53

x_29

===

_477

106o

===

1537

Most minds find this method too much of a strain, though. A simpler way is to multiply the digits one-by-one, first vertically then diagonally, while keeping a mental running total:

5o x 2o = 10oo (total: 10oo)

__53

__29

===

10oo

3 x 9 = 27 (total: 1027)

__53

__29

===

1027

5o x 9 = 45o (total: 1477)

__53

__29

===

1477

2o x 3 = 6o (total: 1537)

__53

__29

===

1537

Using the running total means that you only need to keep track of 3 or 4 numbers at a time. This fits nicely into a tight square of digits which most people should be able to picture without trouble. You can also do these four digit-by-digit multiplications in any order you choose (just remember to do each of them once!).