Shortcut for Multiplying 2 digit numbers

Here in this post I am going to show you some tricks to practice to fasten you calculation mainly based on multiplications. This will help you to face any problems with full confidence and solve calculation process mentally or with a little calculations. The work of shortening the procedure is to be done by the student with the help of practice and also  depending on his calibre and speed as in this post I am going to elaborate each and every concept of multiplication of 2- digit natural numbers under some special cases,

in very detail manner with the help of which you will be able to understand and solve the problems of this type self without any help.

Let’s continue with this chapter............

Special Cases:-

 Type 1^st  :- Single Line Multiplication (2 – digit Numbers by 11) {a b × 11}

                                    a(tenth place digit) b (unit place digit) × 11.

                                                                                                                                                    

Box no. 3rd         a

Box no. 2nd     a + b

Box no. 1st          b

              

      =     Product   

This type of multiplication is actually addition based rather than multiplication.

Step 1^st :- Find b, write it in box no. 1^st.

Step 2^nd :- Find { a + b.}. If it is a one – digit number write it in box no. 2^nd. If it is a two – digit number then write its units digit in box no. 2^nd and carry over the rest.

Step 3^rd :- Find {a + carried over if any.}. Write this result in box no. 3^rd.

Step 4^th :- Read the number so obtained from left to right. This number is the required product.

Example :-

           (i)          Find the product of 56 and 11.

Solution :-  

56 × 11

Box no. 3rd          6

Box no. 2nd         1

Box no. 1st           6

               

    =   Product 

Step 1^st :- 6, we write 6 in box no. 1^st.

Step 2^nd :- {5 + 6 = 11.}. We write 1 in box no. 2^nd and carry over 1.

Step 3^rd :- {5 + 1 = 6.}. We write 6 in box no. 3^rd.

Step 4^th :- The required product 616.

Example :-                        

             (ii)        Find the product of 64 and 11.

Solution :-  64 × 11

Box no. 3rd          7

Box no. 2nd         0

Box no. 1st           4

                

  =  Product 

Step 1^st :- 4, we write 4 in box no. 1^st.

Step 2^nd :- {6 + 4 = 10.}. We write 0 in box no. 2^nd and carry over 1.

Step 3^rd :- {6 + 1 = 7.}. We write 7 in box no. 3^rd.

Step 4^th :- The required product 704.

Type 2^nd :- To multiply 2-digit natural number (a  b) and  2- digit natural number(a  c).

To apply this trick of multiplication between two 2-digits natural numbers the following two conditions must be fulfilled :-

·         The sum of unit digit of those numbers must be 10.

·         The rest digits (left to the unit digit) are same in both the numbers.

        a(tenth place digit) b (unit place digit) × a(tenth place digit)  c(unit place digit).

Box no. 2nd a × (a + 1)

Box no. 1st b × c

    =    Product        

Step 1^st :- Find b × c. If it is a one-digit number, then convert it to two- digit number by prefixing 0 and write it in box no. 1^st. If it is a two – digit number, then write it in box no. 1^st.

Step 2^nd :- Find { a × (a + 1)}. What so ever you get just write it in box no. 2^nd.

Step 3^rd :- Read the number so obtained from left to right. This number is the required product.

(Note this method of multiplication is applicable only and only if the above mention two conditions are fulfilled otherwise apply the base rule of three boxes only.)

Example

          (i)        Find the product of 38 and 32

Sol. :- The given two numbers fulfil the two basic required condition :-

·         The sum of unit digit of these numbers (8 + 2 = 10).

·         The rest digits (left to the unit digit) are same (3) in both the numbers.

Box no. 2nd  12

Box no. 1st 16

     =     Product      

Step 1^st :- Find 8 × 2 = 16. as it is a two – digit number, so write it in box no. 1^st.

Step 2^nd :- Find { 3 × (3 + 1) = 3 × 4 = 12}.  just write (12) in box no. 2^nd.

Step 3^rd :- The required product 1216.

Example          (ii)       Find the product of 81 and 89.

Sol. :- The given two numbers fulfil the two basic required condition :-

·         The sum of unit digit of these numbers (1 + 9 = 10).

·         The rest digits (left to the unit digit) are same (8) in both the numbers.

Box no. 2nd  72

Box no. 1st 09

    =     Product      

Step 1^st :- Find 1 × 9 = 16. as it is a one – digit number, so prefix it with 0 as (09) and write it in box no. 1^st.

Step 2^nd :- Find { 8 × (8 + 1) = 8 × 9 = 72}.  just write (72) in box no. 2^nd.

Step 3^rd :- The required product 7209.

Note you may say that this is so long but dear this is the only way to explain the whole concept of the question to you now its upto you that how fast and short handedly (or mentally) you can solve these type of questions)

More types of questions will be followed soon on this blog........................