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1. If 302=23, 403=229 then 504=?

  1. If 302=23, 403=229 then 504=?

solution:

Here we should know the powers of each number:

in the first thing the logic was 3x3-2x2=23

in the second thing the logic was 4x4x4x4 - 3x3x3=256-27=229

so, last one 5x5x5x5x5 - 4x4x4x4=3125-256=2869

Multiplication of a number with same number of 9's

 Here we go with one more trick in this post we are going to see as the title suggests Multiplication of a number with same number of 9's

Here we go into the trick let's see

With ease we are going to learn the trick very simple so move reading down.

Let's take simple numbers,

34 x 99=?

see here the answer is 3366

If you know this trick you would be saying that answer in no time so, let's get into the trick with out any delay.

Steps to follow in order to achieve this answer is as follows:

1. Take the number 34 subtract 1 from it. It gives 33 ( which is our first part of answer )
2. Now subtract this 33 from 99 which gives us 66 ( This can be considered as the complement number for 99)
3. combine both the results we get the answer. As easy as it looks

now, lets check this with following images 

We have taken 34 x 99 check the above picture 

We have subtracted 1 from it which gives us 33

Then we subtracted 33 from 99 we get 66

Now we combined both the answers and we got 3366 as our answer you can check this with calculator or by simple multiplication.

Now you can check for any numbers of your own try out and before to that let's take a test on the things which we have seen so that it is concretized 

click below text which is in inverted commas

"Check your learning"

 There can be some small modification possible in the above steps to make the trick more easier can you find out....., inform me through comments if you found.

quiz is here

Keep learning.......,

Multiplication of numbers ending with 5

 Here is one more trick to work on,

Multiplication of numbers ending with 5.

Points to Note in here is that

One must know the Addition, Subtraction, Multiplication, Division  to do this trick

Trick goes like this step wise:

1. We have to multiply the ten's digits
2. We have to add the ten's digits
3. We have to divide the result obtained after adding by 2
4. Main point is that on dividing the result by 2 if we get a result which is in decimals then we have to keep 75 at last of our answer otherwise 25
5. Add that number before the decimal to the multiplication result 
6. write down the answer in the first of our result 
7. We get the answer

                                                              Are the steps clear 

If not check  continue to reading below

Step 1: Identify the Ten's Place digits in this case 1 and 2( as we have taken 15x25=?)

Step 2: Multiply the ten's digits and keep the answer aside (1 x 2=2)

Step 3: Add the Ten's digits and keep the answer aside (1+2=3)

Step 4: Now take out the step 3 result and divide it by 2 (3/2=1.5) which gives us 1.5 here

Step 5: Now observe that we got quotient on dividing in decimal so we have to write 75 as the second part of our answer see below.

Step 6: Now again observe that we got a decimal so the number before he decimal which is 1 in this case has to be added to the step 2 result which is 1 x 2=2 we get 3           (3=1 +2)

Step 7: Now we got the answer by keeping the result from step 6 as a first part of our answer

We got answer 325

so, 15 x 25 =325

For continuous flow of explanation watch the video given below

Hope you got cleared 

Now let's check with bit bigger numbers

let's take 

135 x 35 =?

1.  13 x 3=39

2. 13 + 3=16

3. 16/2 =8     

4. 8 + 39= 47 (our answers first part)  

5. we got non-decimal (Integer) so 25 at last (second part)

6. The answer we obtain is 4725

check out in calculator

and this gif too

Check what you have learnt by clicking the words in inverted 

":Test yourself "

Thank you  :-)

Keep Learning..........., 

Multiplication of numbers who units digits sum is 10

 Hi, Here I come up with one more trick in multiplication which is multiplication of 

Numbers ending with digits whose sum is 10 and Have same ten's digits

 As usual let's take two number easy numbers which are 

12 x 18=?

Are you taking some time are taking some paper to multiply, You would not in need of these things if you read this page once, I say the answer is 216.  How? below is the answer for this How.

Step 1: Identify the basic

We have ten's digits same which is 1

So, we are going to see what is the next number of 1, Yes, it is true 2 is the next number of 1

Step 2: Proceed Further

Multiply the two number which we found in the previous step Which are 1 and 2

so, 1 x 2 =2

This will be our first digit in our result you can observe.

Step 3: Go for the main observations

Now, observe the units digits which are 2 and 8 in this case You also observe that these two numbers sum is 10 (2+8=10) correct right.

NOTE: This is necessary condition for this trick ( tens digits sum should be 10)

Step 4: Multiplication of numbers

 Now multiply the ten's digits 2 x 8=16

This becomes our second part of the answer. Observe please

Step 5: Placing all in place

Now the result obtained in the Step 2 and Step 4 join together we get our answer as 216

It is as simple as it is said.

so the answer for 12 x 18 is 216

End of process

Now, check out this trick with other numbers as well 

See the below video made by kids to see few more examples and kinds in it

To watch Video click me

Now let's check this trick with some other three digit numbers as well

Here we go, 

First to apply the trick we have to check whether the units digits sum is 10 or not, above picture shows it is.

This picture is evident to say that we can apply the trick.

Step 1 is applied here so here we go multiplying the units digits 7 x3=21,

The result obtained in the step one serves as the last part of our required answer so see the above and below pictures to connect with the words.

Now time to go for the further steps Which is multiplication of the ten's and hundred's digits 

Here we are using the technique which we have already seen in the last blog which is multiplication of numbers ending with 1. Which goes like this we have 21, 21 in the 10's and 100's digits respectively.

On multiplying 21 x 21=441 by using trick (2x2)(2+2)1.

This serves as the one more part of our answer which as shown in the above picture.

 

Hope you have understood it, 

If you still have a doubt in it follow the gif below

If your doubt still persists please ask me in the comments section.

have a good day... :-)

Knowledge stops where Learning stops

so,  Keep learning.

Numbers ending with 1 trick

 When you are asked with some calculations on of a sudden it is sometimes difficult to say but it is not always that we can't say in such situations these tricks will be helpful for quick solving of calculations with mind.

In this promotion of simple tricks this is the second on among those The trick which goes on Numbers ending with 1 ( the numbers whose unit digits are 1)

Ex: 21 x 21

If I would have asked you the 11 x 11 = ? then you would have quickly responded without a delay If you have studies my previous blog. No problem though here we go with the trick.

11 x 11 =121

21 x 21=441

31 x 31=961

41 x 41=???

51 x 51=???

Did you get the trick...., If yes very good, If no still good because we will learn it now. 

see the pictures give below to know it easily.

Step1:

We take the first ( ten's place digits) and then 

Step2:

We multiply them and keep it as a 1st digit of your answer here in this case it is 9

Step 3:

We add the ten's place digits here in this case 3 in the question and place the result (6) as the second digit of your answer. Your first digit will be the result of step 2 which is 9 in this case and the second digit will be 6. 

Step 4: 

Keep the last digit as 1 only

Now above picture shows us the case where we get two digit when we add 

Here we added the ten's place digits which are 5 on adding we got result as 10

now , what we do is that carry forward that 1 in 10 to 25 ( which we got after multiplying)

so, it becomes 26 and remaining 0 as the next digit (see the picture)

If you still have a doubt see the video below

Now it holds for any other numbers also for instance check the below picture and understand

In here we have taken 151 x 31 here we got to see that 15x 3 is 45

and 15+3 is 18 so on taking 1 as carry forward to 45 we get 46 and 

left out 8 after 46 and as usual last 1

then we get 4681 as the result you can check that in calculator if you want

you can verify all these

click this to-------> "CHECK OUT WHAT YOU HAVE LEARNT"

after that click back to return this page again.

11 multiplication Trick

Let's see how can we make calculations easy by using few tricks which are very simple. Let's just dive into the pool and swim it out: 

let's become Einstein for a while 

I request you to practice the trick to convert your self into Einstein just for a while *conditions apply

let's see

11 x ( Multiplication any number with 11)

let's check it out suppose

11 x 12 = 132

11 x 13 =143

11 x 14 = 154

11 x 15 = 165

observe the pattern and try finding out the trick yourself.......,