Maths Tricks

## Square of 2 digit number (Short Trick)

There are number of tricks to find square of any 2 digit number so have a look at some of them.

Trick No. 1 :- Let me explain the rule of finding square of any 2 digit number with the help of some examples.

Example 1.  Suppose we want to calculate square of 47.

Solution :-    472 = (47+3)*(47-3)+32

= (50*44)+9 = 2200+9 = 2209

In this method, we have to make a number ending with 0, that’s why; we add 3 to 47.

Example 2.  Suppose we want to calculate square of 75.

Solution :-     752 = (75+5)(75-5)+52

= (80*70)+25 = 5600+25 =5625

Similarly , we added 5 to 75.

Comment below in case you find any problem in this technique.

Trick No. 2 :- We all know how to calculate square of any number by regular method. That is if we want to calculate for 99 then we will multiply both the numbers and get the result as 9801. But regular method takes precisely more time than the method i am going to discuss here.

Lets understand this method with some examples :-

Example:- Find the square of 99

Solution:-

•  In order to find the square of 99 we would select a number greater than 99 and is nearest to it. In this case that number is 100.
• Now we will subtract (2 x 99 x 1) +(1)2 from the square of selected number i.e., from 10000.
• The one in above line is from  100 – 99 here.
• Hence the equation will look like (100)2-[(2x99x1)+1].
• Which is equal to 10000 – 199 = 9801.

Hence the result is 9801.

Lets take one more example

Example:- Find the square of 87

Solution:-

•  In order to find the square of 87 we would select a number greater than 87 and is nearest to it. In this case that number is 90.
• Now we will subtract (2 x 87 x 3) +(3)2 from the square of selected number i.e., from 10000.
• The 3 in above line is from  90 – 87 here.
• Hence the equation will look like (90)2-[(2x87x3)+9].
• Which is equal to 8100 – 531 = 7569.

Hence the result is 7569.

The above method is far better than the method we are using till date. So a little bit practice by using this method will save your time in competitive exams as compared to other students.

In case if there is any doubt in these method please let us know in the comment box below. We are happy to help you all.

Maths Tricks

## Multiply By 11

This technique teaches you how to multiply any number by 11, easily and quickly. we will take a few examples and from these you will see the pattern used and also how easy they are to do.

So, to begin let’s try 12 times 11.

First things first you will ignore the 11 for the moment and concentrate on 12.

Split the twelve apart,like so:

# 1<–>2

Add these two digits together 1+2 = 3

# 1+2 =3

Place the answer, 3 in between 12 to give 132

11*12 = 132

Let’s try another:

48*11

again, leave the 11 alone for a moment and work with 48

# 4+8 = 12

So now we have to put the 12 in between the 4 and 8 but don’t do this:

4128 as that is wrong…

First, do this; Place the 2 from the twelve in between the 4 and 8 giving 428.

Now we need to input the 1 from the twelve into our answer also, and to do this just add the one from 12 to the 4 of 428 giving 528!

## Multiply By 12

Here is a trick to multiply any 2 digit number by 12 which is far better than regular method so have a look at it.

So how does the 12’s shortcut work? Let’s take a look.

12 X 7

the first thing is to always multiply the 1 of the twelve by the number we are multiplying by, in this case 7. So 1 X 7 = 7.

Multiply this 7 by 10 giving 70. (Why? We are working with BASES here. Bases are the fundamentals to easy calculations for all multiplication tables.)

Now multiply the 7 by the 2 of twelve giving 14.

Add this to 70 giving 84.

Therefore 7 X 12 = 84

Let’s try another: 17 X 12

Remember, multiply the 17 by the 1 in 12 and multiply by 10 (Just add a zero to the end):

1 X 17 = 17, multiplied by 10 giving 170.

Multiply 17 by 2 giving 34.

Add 34 to 170 giving 204.

So 17 X 12 = 204

lets go one more 24 X 12

Multiply 24 X 1 = 24. Multiply by 10 giving 240.

Multiply 24 by 2 = 48. Add to 240 giving us 288

24 X 12 = 288 (these are Seriously Simple Sums to do aren’t they?!)

## Multiplication of two numbers that differ by 2

This trick only works if you have memorised or can quickly calculate the squares of numbers. When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.

Let me explain these rule with the help of some examples.

Example 1. Suppose we have to multiply 14 and 16

Solution :- For that just take the square of smaller number and substract one from it. Like This

14 * 16 = (14+1)2 – 1 = 225-1 = 224

Example 2. Suppose we have to multiply 28 and 30

Solution :- Similar as above

28 * 30 = (28+1)2 – 1 = 841-1 = 840

## Same Base Method

When both the numbers are more than the same base.

Example 1: 12 × 14

Step 1: Here base is 10
12 + 2 [12 is 2 more than 10 also called surplus]
14 + 4 [14 is 4 more than 10 also called surplus]

Step 2: Cross add: 12 + 4 =16 or 14 + 2 = 16,(both same) which gives first part of answer = 16

Step 3: Vertical multiplication: 2 × 4 = 8
So, 12 + 2
14 +4
16 / 8So, 12 × 14 = 168(14 + 2 = 12 + 4)

Example 2: 105x 107

Step1: Here base is 100
105 + 05 [105 is 5 more than 100 or 5 is surplus]
107 + 07 [107 is 7 more than 100 or 7 is surplus]
Base here is 100 so we will write 05 in place of 5 and 07 in place of 7

Step 2: Cross add: 105 + 7 = 112 or 107 + 5 = 112 which gives first part of the answer = 112

Step 3: Vertical multiplication: 05 × 07 = 35 (two digits are allowed)
As the base in this problem is 100 so two digits are allowed in the second part.
So, 105 × 107 = 11235

Both numbers less than the same base

Example1: 99 × 98

Step 1: Check the base: Here base is 100 so we are allowed to have two digits on the right hand side.
99 – 01 (1 less than 100 ) i.e. 01 deficiency
98 – 02 (2 less than 100) i.e. 0 2 deficiency

Step 2: Cross – subtract: 99 – 02 = 97 = 98 – 01 both same so first part of answer is 97

Step 3: Multiply vertically – 01 × – 02 = 02 (As base is 100 so two digits are allowed in second part
So, 99 × 98 = 9702

Example 2 : 89 × 88

Step 1: Here base is 100
So, 89 – 11 (i.e. deficiency = 11)
88 – 12 (i.e. deficiency = 12)

Step 2: Cross subtract: 89 – 12 = 77 = 88 – 11(both same)
So, first part of answer can be 77

Step 3: Multiply vertically – 11 × – 12
Again to multiply 11 × 12 apply same rule
11 + 1 (10 + 1)
12 + 2 (10 + 2)
11 + 2 = 13 = 12 + 1 / 1 × 2 = 12 so, 11 × 12 = (1) 32 as only two digits are allowed on right hand
side so add 1 to L.H.S.
So, L.H.S. = 77 + 1 = 78
Hence 89 × 88 = 7832

These are very simple tricks as compared to regular method of multiplying each numbers hence a little practice of this trick will save our time in competitive exams. If you find any difficulty regarding any of these tricks please let us know in the comment box below.