You must have tried to solve or calculate large numbers in your head. But it is not so easy. It takes too much time and chances of mistakes are even high. Do you know, the reason? It is not that you don’t know the basics like addition, subtraction or multiplication etc. The problem is, the method you use to add, subtract or multiply numbers is useful if you are using a pen and paper. We all have learnt mathematics in our school time. We had used pen and paper to practice and solve all those calculations. But that method will not work if you are doing it in your head.

There is completely a different way to do this. Yes it is right… there is a different method to do all those calculations in your head. But remember… it is just a method, not a trick. It is like learning a few basic concepts about mathematics and using those concepts for different calculations, again and again. I want to share these concepts with you.

### Think Left to right

We read all numbers from left to right. So our mind can remember and understand numbers in left to right order, much better than right to left. For example if we are solving 1500+25, on paper we will add 0 & 5 first (right to left) but if you want to do it in your head, you must add it from left to right to do it easily.

### Product of 11 & 2 digit number

It is very simple to multiply any 2 digit number with 11. Suppose you want to multiply 25 with 11. Just write the number 25 with some space in between like 2__5 and write the sum of both digits in middle of these two numbers as 275.

**Example 24 x 11** = Just write the sum of 2 & 4 in the middle of 2 & 4.

Sum of 2 & 4 is 6. So here we write 264.

**Example 81 x 11** = Just write the sum of 8 & 1 in the middle of 8 & 1.

Sum of 8 & 1 is 9. So here we write 891.

What to do if the sum of two digits is greater than 9? Suppose we want to multiply 85 with 11. Here the sum of two digits 8 & 5 is 13 which is greater than 9. In this case you have to carry the extra digit 1 from 13 and add it to the first digit 8. So the answer is 935.

**Example 47 x 11** = 4 (4+7) 7 = 4 (11) 7 = now carry 1 from 11 to 4 like 517.

**Example 59 x 11** = 5 (5+9) 9 = 5 (14) 9 = now carry 1 from 14 to 5 like 649.

### The product of 11 and any 3 digit number

If you want to multiply 11 with any 3 digit number just write the sum of “first and second digits” & the sum of “second and third digits” in the middle of first and third digit.

**Example**, you want to multiply 11 with 123. It is 1 (1+2) (2+3) 3 so, 1353.

**Example 254 x 11** = 2 (2+5) (5+4) 4 = 2794

If the sum of digits is greater than 9, use the same method of carry over as you have learnt in case of 2 digits number.

**Example 877 x 11** = 8 (8+7 )(7+7) 7 = 8 (15)(14) 7

Now carry 1 from 15 to 8 = 9 (5)(14)7

Now carry 1 from 14 to 5 = 9 (6)(4) 7

So the answer is 9647.

**Example 678 x 11** = 6 (6+7)(7+8) 8 = 6 (13)(15) 8

Now carry 1 from 13 to 6 = 7 (3)(15) 8

Now carry 1 from 15 to 3 = 7 (4)(5) 8

So the answer is 7458.

### Square a 2 digit number that ends in 5

It is too easy. Just multiply the first digit in the number by the next higher digit then attach 25 at the end. If you want to calculate square of 65 then multiply the first digit 6 by the next higher digit (which is 7) and attach 25 at the end. 6 x 7 is 42, attach 25, so the answer is 4225.

**Example square of 45** is 4 x 5 attach 25 = 2025

**Example square of 95** is 9 x 10 attach 25 = 9025

### Multiply 2 digits number that have same first digits & last digits sum is 10

If you want to multiply 2 digits that have same first digits and sum of last digits is 10 then multiply the first digit by the next higher digit, than attach the product of last digits.

**Example 67 x 63**

We have two digits 67 and 63. The first digits of theses numbers are same (6) and sum of last two digits (7+3) is 10. So we can apply this method here.

Multiply the first digit 6 by the next higher digit which is 7 = 6 x 7 = 42, and attach the product of last 2 digits in the end which is 7 x 3 = 21, so the answer is 4221.

**Example 48 x 42** = 4 x 5 = 20 and attach 8 x 2 = 16 at the end, so answer is 2016

**Example 92 x 98** = 9 x 10 = 90 and attach 2 x 8 =16 at the end, so answer is 9016

We will learn about more methods in the next article…. keep subscribed.

*Thanks.*

Nice

Thank you.