Multiplication of Numbers 

Multiplication of Numbers by Short Cut  Methods 

1) Multiplication by 9, 99, 999, 9999

                       Rule :-

  Place as many zeros to the right of the multiplicand as is the number of nines and from the number so formed , subtract the multiplicand to get the answer .

                  

Example :-

a) Multiply 5763 by 9

     5763 X 9 = 57630

                      -   5763

                  ---------------

  Answer        51867

b)Multiply 5763 by 99

   5763 X 99 = 576300

                       -     5763

                  -----------------

Answer           570537

c) Multiply 5763 by 999

    5763 X 999 = 5763000

                          -       5763

                         ----------------

Answer              5757237

d) Multiply  5763 by 9999

      5763 X 9999 = 57630000

                               -        5763

                              ____________   

Answer                  57624237                

2) Multiplication by 11 

     Rule :         

Step 1     0 + unit digit

Step 2     unit digit + tens digit

Step 3     tens digit + hundredth digit                Step 4     hundredth digit + thousands digit

          :

          :

          :

                last digit  +  0  .

eleven has two digits so that we can add maximum two digit .

 we assemble these steps like

[step 4 ]  [step 3]  [step 2]  [step 1] 

Example :-

a) Multiply  234 by 11

    234 X 11 = 0+2/2+3/3+4/4+0  

                    =  2574

b) Multiply   34567 by 11

    34567 X 11 

                         = 0+3/3+4/ 4+5/5+6/ 6+7/ 7+0

                         = 380237

c) Multiply  45678932145 by 11

     45678932145 X 11

=0+4/4+5/5+6/6+7/7+8/8+9/9+3/3+2/2+1/1+4/4+5/5+0

= 502468253595

d) Multiply  987654321899765432 by 11

     987654321899765432 X 11

= 0+9/9+8/8+7/7+6/6+5/5+4/4+3/3+2/2+1/1+8/8+9/9+9/9+7/7+6/6+5/5+4/4+3/3+2/2+0

= 10864197540897419752

3) Multiplication by 111

     Rule :-  

Step 1  0 + unit digit 

Step 2  unit digit + tens digit 

Step 3  unit digit + tens digit + hundredth                     digit 

       :

       :

              last digit + 0

one hundred eleven has three digit so that we can add maximum three digit .

we assemble these step like

[step 3] [step 2] [step 1]

Example :-

Multiply 3256 by 111

 3256 X 111

= 0+3/3+2/3+2+5/2+5+6/5+6/6+0

=361416

4) Multiplication by 1111

    Rule :-

Step 1  0 +  unit digit

Step 2  unit digit + tens digit

Step 3  unit digit + tens digit + hundredth                   digit

Step 4  unit digit + tens digit + hundredth                     digit + thousand digit

        :

        :

        : 

last digit + 0

Example :-

Multiply  3256 by 1111

3256 X 1111

= 0+3/3+2/3+2+5/3+2+5+6/ 2+5+6/5+6/6+0

=3617416

5) Multiplication by 12

    Rule :-

Step 1  2 X unit digit  +  0

Step 2  2 X tens digit  + unit digit

Step 3  2 X 0 + tens digit

Example :-

a) Multiply  14 by 12

14 X 12

= Step 1     2 X 4 + 0 =  8

   Step 2     2 X 1 + 4 =  6

   Step 3     2 X 0 + 1 =  1      

we arrange the step in sequence

[Step 3 ] [Step 2 ] [step 1]

   Answer =168

b) Multiply  15 by 12

15 X 12

= Step 1    2 X 5 + 0 = 1/0

   Step 2    2 X 1 + 5 = 7

   Step 3    2 X 0 + 1 = 1

we arrange the step in sequence

[step 3 ] [step 2 ] [step 1 ]

Answer  = 180

 6) Multiplication by 5

Rule :-

If we multiply a number by 5 ,we put zero right side a number and divide by 2.

Example :-

85 X 5 =  850/2 =425

66 X 5 =  660/2 =330

8765 X 5 = 87650/2  =43825

7) Multiplication by 25

Rule :-

If we multiply a number  by 25 , we put double zeros right side a number and divide by 4 .

Example :-

85 X 25 = 8500/4 = 2125

66 X 25 = 6600//4 =1650

8) Multiplication by 125

Rule :-

If we multiply a number by 125 ,we put three zeros right side a number and divide by 8 .

Example :-

85 X 125 = 85000/8 =10625

89765 X 125 =89765000/8 = 11220625

9) Multiplication by 625

Rule :- 

If we multiply a number by 625 , we put four zeros right side a number and divide by 16.

Example :- 

4678 X 625 = 46780000/ 16 = 2923750

2348 X 625 = 23480000/16 = 1467500

10) Multiplication of two digit numbers

Rule :-

                A  B

            X  C  D

---------------------------------------------

[A X B ]   [ A X D + B X C ]  [ B X D ]

Step (3)          Step (2)           Step (1)

Example :- 

a)  32 X 52

                    3    2

               X  5    2

--------------------------------------------------

3 X 5    /    3 X 2 + 5 X 2    /    2 X 2

15        / 16                        /   4

Answer = 1664

b)  35 X 74 

                    3        5

            X     7        4

----------------------------------------------------

3 X 7   / 3 X 4 + 7 X 5     /     5 X 4

21       / 47                      / 20

Answer = 2590

11) Multiplication of three digit numbers

Rule :-

                A    B    C

       X      D    E    F

-----------------------------------------------------------------

A X B / A X E + B X D / A X F + C X D + B X E / Step (5)/ Step (4)        / Step (3)                                     

B X F + C X E / C X F

Step (2)        / Step (1) 

Example :-

                     2    3    4

               X    4    5    6

--------------------------------------------------------------------

2 X 4/ 2 X 5 + 3 X 4/ 2 X 6 + 4 X 4 + 3 X 5/ 4 X 5

Step(5)/Step (4)    /  Step(3)                     /Step(2)

+ 3 X 6 / 4 X 6

            / Step(1)

Answer   106704

 

 Exercise

1) 124 X 11

a) 1365    b) 1164    c) 1264    d) 1364

2) 14 X 98

a) 1365    b) 1312    c) 1372    d) 1365

3) 36 X 73

1) 2526    b) 2628    c) 2627    d)     2629

4) 5555 X 9

a) 49995    b) 4959    c) 49959    d) 4955

5) 675 X 675

a) 455625    b) 45645    c) 455321    d)45625 

Answer    1) d    2) c    3) b    4) a    5) a