Our first multiplication trick applies to multiplying two digit numbers close to base ten. while this quick multiplication trick works for any two digit number, only 11-19 calculate easily in your head.
This trick is as follows:
our problem: 12 x 14 =
we solve this question first by taking our first two digit number: 12 and add the last digit of the second two digit number: 4. 12 + 4 = 16.
The first 2 digits of our sum will be the product of this answer: 16
now we will take the last digit of both numbers and multiply them: 2 x 4 = 8
This product will be the final digit of our number: 168
12 x 14 = 168
Now, what if our final digit gives us a product greater than 9.
Consider this example.
13 x 19
as with the first example, we add 13 and 9 to get the sum of 22. These will be the first two digits of our number: 22
our second step is to now multiply the last digit of both numbers with each other: 3 x 9 = 27
we need to, in this case carry our numbers. so, 22 and 27 now turns out to be 247, this is because we can not have anything greater than a three digit numbers unless we are multiplying numbers in excess of 30.
The final product of this equation is 247.
While this trick works easily in your head, it is best to just keep it to numbers multiplied close to ten.
In order to multiply two digit numbers by two digit numbers in your head that are more than 20 there is a far easier way than that of our last example.
please follow.
Our example: 23 x 42
first to get our first digits we multiply the first two digits of each of our two digit numbers: 2 x 4 = 8
This number will be the first digit of the product. 8
for the final digits we will multiply the last two digits of each number by each other: 3 x 2 =6
This number will be the final digit in the product.
Our product should look like this so far: 8X6
For our final digit which will be between the first two we placed all we do is multiply the digits furthest from eachother and the digits closest to the middle seperately and then add both products together. This should look like 2 x 2 = 4 and 3 x 4 = 12. now we need to add these products together. 4 + 12 = 16.
So the middle digit will be 6 and we need to carry the one over to our first number. Our product for the equation will be 966.
23 x 42 = 966
We’ll try one more example now so that you can firmly plant in your mind the process of mentally finding the answer to this equation of multiplying two digit numbers by two digit numbers.
Our final example problem.
56 x 63
First we multiply the first digits of these two numbers: 5 x 6 = 30
Then we multiply the final digits of these two numbers: 6 x 3 = 18
our product will look like this so far 3018
we then will multiply the digits furthest from the middle and then the digits closest to the middle seperately: 5 x 3 = 15 and 6 x 6 = 36 we now take the product of these two equation and add them together: 15 + 36 = 51.
Now plug this number into the middle of our product and carry the first digit over. The product will now look like this 3528. To clarify, we added the two digits in the third place to eachother essentially carrying over our final digit in the equation.
While this second trick may seem complicated at first, with a little practice you should be able to calculate most two digit numbers in your head in abut 6-8 seconds. What will help immensely, that is if you have not already done so, is memorizing your multiplication table.
feel free to check out my other articles in this series of Mental Math Tricks!
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