MULTIPLICATION

I suggest you to remember the tables up to 9 because it saves some valuable time during calculation.

Let us look at the case of multiplication by a number more than 10

5892 X 11

05892 X 11

STEP I    :(2 X 1)                  = 2

STEP II   :(9 X 1)+2             =¹12

STEP III :(8 X 1)+9+1        =¹812   

STEP IV :(5 X 1)+8+1        =¹4812

STEP V  :(0 X 1)+5+1        =64812

5324 X  12

05324 X 12

STEP I    :(4X 2)                   =8

STEP II   :(2 X 2)+4             =88

STEP III :(3 X 2)+2             =888  

STEP IV :(5 X 2)+3             =¹3888

STEP V   :(0 X 2)+5+1       =63888

If you go through it yourself you will find that calculation goes very fast and easy…

17 x 18

                            STEP I        : (7 X 8) = ⁵6

                            STEP II       : (1 X 8)+ (7 X 1) = ²06

                            STEP III     : (1 X 1)+2=306

                            AN OTHER METHOD 18 ROUND FIGURE IS 20 (18+2)

                            17 X 20=340

                            17 X 2 = - 34

                                ANS: 306

87 X 92

                            STEP I        : (7 X 2) = ¹4

                            STEP II       : (8 X 2)+ (7 X 9) = ⁸04

                            STEP III     : (8 X 9)+8=8004

                            AN OTHER METHOD 92 ROUND FIGURE IS 100 (92+8)

                            87 X 100=8700

                            87 X 8 = -696

                                ANS: 8004

Try some question yourself

Let's go for some difficult questions like

69712 X 641     4562 X 345

Don’t worry when I am here to solve above problems in easy way

Method I

I^st calculate 69712 X 640 =44615680 (Do like above)

             Add 69712 x 1               69712

                                          __________

                                              44685392

Method II

 69712 X 641

Step I  (2 X 1)                                    =2       

Step II    (1 X 1)+(2X4)                     =92

Step III   (7X1)+(1X4)+(2X6)            =²392

Step IV  (9X1)+(7X4)+(1X6)+2       =⁴5392

Step V   (6X1)+(9X4)+(7X6)+4       =⁸85392

Step VI               (6X4)+(9X6)+8       =⁸685392

Step VII                          (6X6)+8       =44685392

4562 X 345

Method I

I^st calculate 4562 X 340 =1551080 (Do like above)

             Add 4562 x 5            22810     

 __________

                                            1573890           

Method II

4562 X 345

Step I     (2 X 5)                                 =¹0     

Step II   (6 X 5)+(2X4)+1                  =³90

Step III  (5 X 5)+(6X4)+(2X3)+3      =⁵890

Step IV  (4 X 5)+(5X4)+(6X3)+5     =⁶3890

Step V                (4X4)+(5X3)+6      =³73890

Step VI                            (4X3)+3     =1573890

These techniques are for Mental Maths. You should do calculations in your mind only.

1.    Multiplication using multiples

Assume that we should find out the result of 12X15. 

12 x 15   (Here we can write this 15 as 5x3)

=  12 x 5 x 3 (now 12x5 becomes 60)

=  60 x 3 (For this you just calculate 3x6, that is 18 and add one Zero to it. that is 180)

=  180

2.    Multiplication by distribution 

Assume that we should find out the result of 12x17

12 x 17  

(Here we can divide this 17 as 10+7. here, multiplying 12 with 17 is same as multiplying 12 with 10 and 7 separately and then adding the results)

so, we can write it as

= (12 x 10) + (12 x 7) 

= 120 + 84

= 204 

3.    Multiplication by "giving and taking"

12 x 47  (Here its little difficult for us to calculate the multiplication of 12 and 47 mentally. so just check for the ROUNDED number nearer to 47. Yes it is 50. so.....

= 12 x (50 - 3) 

= (12 x 50) - (12 x 3)   = 600 - 36

= 564

4.    Multiplication by 5

If we have to multiply a number with 5, just divide the number with 2 and then multiply the result with 10. Confused? Its very simple step actually....

428 x 5   (Now just divide the number with 2)

= 428 x 1/2 = 214 (Now multiply it with 10. I mean just add a zero at the end :P)

= 214 x 10

= 2140 (This is our result)

What’s the logic behind this step? 

Very simple. 

Lets say the number is X.

 Now we are dividing the number with 2.  so here X becomes X/2. 

 And then we are multiplying it with 10.  So it will become 10x / 2  

Now cancel it with 2. so it becomes 10x / 2 = 5X = 5 multiplied by X. That’s it ;)

5.    Multiplication by 10  ------------  just move the decimal point one place to the right

16 x 10

= 160

5.9 = 159

169.93 = 169.3  

6.    Multiplication by 50 ------ divide with 2 and then multiply by 100

Well, this is also same process as we did for 5. Here we should add an extra zero. That’s it

18 x 50

= (18/2)  = 9

= 9 x 100

= 900

7.    Multiplication by 100 -------- move the decimal point two places to the right

45 x 100

= 4500  

8.    Multiplication by 500-------- divide with two and multiply with 1000 

21 x 500

= 21/2 x 1000

= 10.5 x 1000

= 10500

9.    Multiplication by 25 ---------- use the analogy Rs 1 = 4 x 25 Paise

25 x 14 (just divide the 14 as 10+4)

= (25 x 10) + (25 x 4) 

= 250 + 100 --->  Rs2.50 + Rs1

= 350

10.  Hey one more thing. Here you can use another technique too. Which we have used for multiplication with 5.

Multiplication by 25 -----------  Divide by 4 and multiply by 100 

36 x 25

= (36/4) x 100

= 9 x 100

= 900  

11.  Multiplication by 11 (if sum of digits is less than 10)

72 x 11

= 7+2 =9, it is Less than 10. so,

= place this term 9 between 7 &2

= 792 (That's the answer)

12.  Multiplication by 11 (if sum of digits is greater than 10)

87 x 11

=>  8 + 7 = 15 

because here 15 is greater than 10, first use 5 and then add 1 to the first term 8, 

which gives you the answer

= 957 

13.  Multiplication of numbers ending in 5 with the same first terms (square of a number)

25 x 25 

first term = (2 + 1) x 2 = 6

last term = 25

answer = 625 è square of 25

75 x 75 

first term = (7 + 1) x 7 = 56

last term = 25

answer = 5625 è 75 square