Assume that we should find out the result of 12 x 15.

**12 x 15** (**Here we can write this 15 as 5 x 3)**

= 12 x 5 x 3 (now **12 x 5 becomes 60)**

= 60 x 3 (**For this you just calculate 3 x 6, that is 18 and add one Zero to it. that is 180)**

**2.** __Multiplication by distribution__

Assume that we should find out the result of 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)**

**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) - (12 x 3) = 600 - 36

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)**

= 2140 (This is our result)

**What’s the logic behind this step? **

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__

**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

__7. Multiplication by 100 -------- move the decimal point two places to the right__

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

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

**25 x 14** (**just divide the 14 as 10+4)**

= 250 + 100 ---> Rs2.50 + Rs1

__10. 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 __

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

= 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)**

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

which gives you the answer

__13. Multiplication of numbers ending in 5 with the same first terms (square of a number)__

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

answer = 625 => square of 25

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

answer = 5625 => 75 square