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Friday, November 16, 2012

Multiplying Both Two - Three Digit Numbers

Category: Arithmetic

"Published in Newark, California, USA"

How do you multiply these numbers in a shorter way without using a calculator: 
                        
                     66 x 64

Solution:

Well, we have the technique for that. What is the next number after 6? 7, isn't it? Therefore, 6 x 7 = 42. 42 will be the first two digits of the number.

                     4 2 _ _

How do you get the next two digits? Well, multiply both the one's digits in order to get the next two digits. Therefore, 6 x 4 = 24. 24 will be the next two digits of the number. The answer is

                     4 2 2 4

Note: There are two conditions in order for you to use this technique:

1. The ten's digits must be the same. In this case, both are starting with 6. 

2. The sum of the two one's digits must be equal to ten. In this case, 6 + 4 = 10.

Now, you know this technique. Let's try another one:

                     21 x 29

Solution:

The first two digits will be 2 x 3 = 6. Since the product is less than 10, the first digit will be 6. The next two digits will be 1 x 9 = 9. Since the product is less than 10, the next two digits must be written as 09. The answer is

                     6 0 9

Can we do this for both three digit numbers? Yes, we can do this also for both three digit numbers as long as the two conditions are followed. Let's try this one:

                   112 x 118

Solution:

As you notice that both numbers are starting with 11. The first digits will be 11 x 12 = 132. To multiply any two digit number by 11, place the first digit as the first digit of the product, place the last digit as the last digit of the product, and the middle digit of the product will be the sum of the two digits. In this case, the middle digit is 1 + 2 = 3. If the sum of the digits is 10 or more, use the ten's digit as a carry over to the first digit. 

The next two digits will be 2 x 8 = 16. Therefore, the answer is 

                    1 3 2 1 6