Base Method Of Multiplication (PART-2)

Are You know what is Base Method of Multiplication?

If you don't know what is it.

Then go to its 1st part and read it.

Case1:

(When the number of digits in RHS exceeds number of zeros in the base.)

Q.950×950=?

A.

• The base is 1000 and the difference is -50. The number of zeros in 1000 is 3 and so the RHS will be filled in by a three digit answer.

• The vertical multiplication (-50 × -50) gives 2500 and the cross answer gives 900. They are filled in as shown above.

• Note that the RHS can be filled by a three-digit answer only but we have a four-digit number, namely 2500.

• We carry over the extra digit 2 to the LHS and add it to the number 900 and make it 902.

• The number on the LHS is 902 and the number in RHS is 500. The final answer is 902500

Q.1200×1020=?

A.

• The base is 1000 and the difference is 200 and 20 respectively

• The vertical multiplication yields a four-digit answer 4000 which cannot be fitted in three places.

• We carry the extra digit 4 to the LHS and add it to 1220 and make it 1224. The final answer is

1224000.

Case2:

(Multiplying a number above the base with a number below the base)

Q.95×115=?

• The base is 100 and the difference is -5 and +15 respectively

• The vertical multiplication of -5 and +15 gives -75

• The cross answer is 110

• At this point, we have the LHS and the RHS. Now, we multiply LHS with the base and subtract the RHS to get the final answer. Thus, 110 multiplied by 100 minus 75 gives 10925.

Case3:

(Multiplying numbers with different bases)

Q.85×995=?

A.

• We multiply 85 by 10 and make it 850. Now, both the numbers are close to 1000 which we will take as our base

• The difference is -150 and -5 which gives a product of 750

• The cross answer is 845 which we will put on the LHS

• Thus, the complete answer is 845750. But, since we have multiplied 85 by 10 and made it 850 we

have to divide the final answer by 10 to get the effect of 85 again. When 845750 is divided by 10 we get 84575

• Thus, the product of 85 into 9995 is 84575

Case4:

(When the base is not a power of ten)

Q.48×48=?

A.Actual base = 100

Working base: 100/2 = 50

In this case the actual base is 100 (therefore RHS will be a two-digit answer). Now, since both the

numbers are close to 50 we have taken 50 as the working base and all other calculations are done with

respect to 50.

The difference of 48 and 50 is -2 and so we have taken the difference as minus 2 in both the

multiplicand and the multiplier.

We have the base and the difference. The vertical multiplication of -2 by -2 gives 4. We convert it

to a two-digit answer and write it as 04. The cross answer of 48 - 2 is written as 46 and put on the

LHS. The answer is 4604.

Now, since 50 (the working base) is obtained by dividing 100 (the actual base) by 2, we divide the

LHS 46 by 2 and get 23 as the answer on LHS. The RHS remains the same. The complete answer is

2304.

(In this system, the RHS always remains the same.)

OR:

Actual base: 10

Working base: 10 × 5 = 50

In this case the actual base is 10 (therefore RHS will be a one-digit answer). Now, since both the

numbers are close to 50 we have taken 50 as the working base. Since, 50 is obtained by multiplying 10

by 5 we multiply the LHS 46 by 5 and get the answer 230. The RHS remains the same. The complete answer is 2304.

Carefully observe both the cases given above. In the first case we took the actual base as 100 and got a working base 50 on dividing it by 2.

 In the next case, we got the actual base 10 and got the working base 50 by multiplying it by 5. The student can solve the problem by either system as the answer will be the same.

Base Method Of Multiplication (PART-1)

Many of you won't know about it.Read The Title again you don't what  is it?

So stay connected with us and read our blogs.

Let us have a look at the procedure involved in this technique of multiplication. I have outlined below the four steps required in this technique.

STEPS:

(a) Find the Base and the Difference

(b) Number of digits on the RHS = Number of zeros in the base

(c) Multiply the differences on the RHS

(d) Put the Cross Answer on the LHS

To understand how the method will work we solve following questions.

Step1: 

The first part of the step is to find the base. Have a look at example A. In this example the numbers are 97 and 99. We know that we can take only powers of 10 as bases. The powers of 10 are numbers like 10, 100, 1000, 10000, etc. In this case since both the numbers are closer to 100 we will take 100 as the base.

Similarly, in example B both the numbers are closer to 10,000 and so we will take 10,000 as the base.

So we Have Found the bases.

We are still on step A. Next, we have to find the differences.

In Example A the difference between 100 and 97 is 3 and the difference between 100 and 99 is 1.

In Example B the difference between 10,000 and 9989 is 11 and the difference between 10,000 and 9995 is 5.

Step2: 

In example A the base 100 has two zeros. Hence, the RHS will be filled in by a two-digit number.

In example B, the base 10,000 has four zeros and hence the RHS will be filled by a four-digit number.

Step3: 

The third step (step C) says to multiply the differences and write the answer in the right-hand side.

In example A we multiply the differences, viz. -3 by -1 and get the answer as 3. However, the RHS has to be filled by a two-digit number.

Hence, we convert the answer 3 into 03 and put it on the RHS.

In example B we multiply -11 by -5 and get the answer as 55.

Next, we convert 55 into a four-digit number 0055 and put it on the RHS.

Step4: 

Step D says to put the cross answer in the left hand side. Let us observe how Step D will be applied

in each of the alternatives.

In example A, the cross answer can be obtained by doing (97 – 1) or (99 – 3). 

In either case the answer will be 96. This 96 we will put on the LHS. But we already had 03 on the RHS. Hence, the

complete answer is 9603.

In example B, we subtract (9989 – 5) and get the answer as 9984. We can even subtract (9995 –11). 

In either case, the answer is the same. We put 9984 on the LHS. We already had 0055 in the RHS.

The complete answer is 99840055.

Let us solve a few examples:

Q.9750×9998?

A.

Since both the numbers are closer to 10000, we take it as the base. The difference between 10000and 9750 is 250 and the difference between 10000 and 9998 is 2. Next, the base 10000 has four zeros and hence the RHS will be filled by a four-digit answer. Next, we multiply -250 by -2 and write the answer as 0500 (converting it into a four-digit number) and putting it on the RHS. 

Finally, we subtract2 from 9750 and put it on the LHS. The final answer is 97480500.

Q.1007×1010?

A.

You can solve it by the above 4 steps.

In the next part we will see the cases of base method of Multiplication.

Square Roots Of Perfect Squares

You May have some knowledge about this trick. But not completely.

To find the square roots it is necessary to be well versed with the squares of the numbers from 1 to 10.

The squares are given below. Memorize them before proceeding ahead.

On the basis of observation of unit digits, we can form a table as given below:

Note: ‘A perfect square will never end with the digits 2, 3, 7 or 8’

Let's know the trick by solving some questions.

Q.Find the square root of 7744?

A.

• The number 7744 ends with 4. Therefore the square root ends with 2 or 8. The answer at this stage is __2 or__8.

• Next, we take the complete number 7744. We find that the number 7744 lies between 6400 (which is the square of 80) and 8100 (which is the square of 90).

The number 7744 lies between 6400 and 8100. Therefore, the square root of 7744 lies between the numbers 80 and 90.

• From the first step we know that the square root ends with 2 or 8. From the second step we know that the square root lies between 80 and 90. Of all the numbers between 80 and 90 (81, 82, 83, 84,85, 86, 87, 88, 89) the only numbers ending with 2 or 8 are 82 or 88. Thus, out of 82 or 88, one is the correct answer.

(Answer at this stage is 82 or 88)

• Observe the number 7744 as given below:

Is it closer to the smaller number 6400 or closer to the bigger number 8100 ?

If the number 7744 is closer to the smaller number 6400 then take the smaller number 82 as the

answer. However, if it is closer to the bigger number 8100, then take 88 as the answer.

In this case, we observe that 7744 is closer to the bigger number 8100 and hence we take 88 as the

answer.

The square root of 7744 is 88.

Q.Find the square root of 2304?

A.

• 2304 ends in 4 and so the root either ends in a 2 or in a 8

• 2304 lies between 1600 and 2500. So, the root lies between 40 and 50.

• Thus, the two possibilities are 42 and 48.

• Lastly, the number 2304 is closer to the bigger number 2500. Hence, out of 42 and 48 we take the bigger number 48 as the correct answer.

Q.Find the square root of 5184 ?

A.

• 5184 ends in 4. So the square root ends in either 2 or 8 (Answer = ____2 or ____8)

• 5184 is between 4900 and 6400. So the square root is between 70 and 80. Combining the first two steps, the only two possibilities are 72 and 78

• Out of 4900 and 6400, our number 5184 is closer to the smaller number 4900 (70 × 70). Thus, we take the smaller number 72 as the correct answer

HOPE you like the Trick.Please comment share and Subscribe.

Criss-Cross System Of Multiplication

If You Think that you can perform Multiplication little faster then this trick prove you fail.

This Trick is known as criss-cross method.

The Urdhva-Tiryak Sutra (the Criss-Cross system) is by far the most popular system of squaring

numbers amongst practitioners of Vedic Mathematics. The reason for its popularity is that it can be

used for any type of numbers.

Ex.23×12

We multiply the digits in the ones place, that is, 3 × 2 = 6. We write 6 in the ones place of the answer.

Now, we cross multiply and add the products, that is, (2 × 2) + (3 × 1) = 7. We write the 7 in the tens place of the answer.

Now we multiply the ones digits, that is, 2 × 1 = 2.

The completed multiplication is:

Let us notate the three steps involved in multiplying a 2-digit number by a 2-digit number.

Let us have a look at the multiplication process involved in multiplying a three-digit number by another three-digit number.

The following are the steps involved in multiplying 4-digit numbers:

Example: 2104 multiplied by 3072

STEP-WISE ANSWERS

(a) (4 × 2) = 8

(b) (7 × 4) + (0 × 2) = 28 (2 carry-over)

(c) (0 × 4) + (0 × 7) + (1 × 2) + (2 carried)=4

(d) (3 × 4) + (0 × 0) + (7 × 1) + (2 × 2) = 23 (2 carry over)

(e) (3 × 0) + (0 × 1) + (7 × 2) + (2 carried) = 16 (1 carry over)

(f) (2 × 0) + (3 × 1) + (1 carried) = 4

(g) (2 × 3) = 6

Hope You like It.Ask Any Question in the comment Box.

Cube Roots Of Perfect Cubes

Every One should know that how much important the math is?

In math the tricks are like 'Lift' with which you can go up without any hardwork.

Todat sessions we will discuss about the cuberoots of cubes.

I think everyone know the follow table

Note:If you have not remembered the just remember its unit digit.

We will be solving the cube root in 2 parts. First, we shall solve the right hand part of the answer and then we shall solve the left hand part of the answer. If you wish you can solve the left hand Part Before the right hand part. There is no restriction on either method but generally people prefer to solve the right hand part first.

Q. Find the cuberoot of 287496?

A.

• We shall represent the number 287496 as 287 496

• Next, we observe that the cube 287496 ends with a 6 and we know that when the cube ends with a

6, the cube root also ends with a 6. Thus our answer at this stage is ___6. We have thus got the right hand part of our answer.

• To find the left hand part of the answer we take the number which lies to the left of the slash. 

In this case, the number lying to the left of the slash is 287. Now, we need to find two perfect cubes between which the number 287 lies in the number line. From the key, we find that 287 lies between

the perfect cubes 216 (the cube of 6) and 343 (the cube of 7).

• Now, out of the numbers obtained above, we take the smaller number and put it on the left hand part of the answer. Thus, out of 6 and 7, we take the smaller number 6 and put it beside the answer of __6 already obtained. Our final answer is 66. Thus, 66 is the cube root of 287496.

Note: You Should always break the number by 3,3,... digit.

Q. Find the cuberoot of 2197?

A.

The number 2197 will be represented as 2 197

• The cube ends in 7 and so the cube root will end with a 3.

We will put 3 as the right hand part of the answer.

• The number 2 lies between 1 (the cube of 1) and 8 (the cube of 2)

• The smaller number is 1 which we will put as the left hand part of the answer. The final answer is

13.

Thanks For Reading This Blog.

Multiplication Of Numbers with a Series Of 1's

This is a very short trick to find out the Multiplication of numbers with Series of 1's.In the previous blog we know the trick about Multiplication of numbers with series of 9's.

Note Down The below questions.

So The Trick is very Small.

Let's solve the 1st question.

Algorithm:

1.Take the unit digit of the number and place as the unitdigit of answer.

2.Add The Digits in ascending manner then descending from the right.

i.e; 1st add 2 digit then 3 digit then 4 digits.

(AS PER NO. OF 1'S)

so here two 1 is available.

3. Add 3+2=5

(If the addition become greater than 10 the pick the 1 to the left digit.)

4.make the Answer 352.

So let's move to the Second question.

Algorithm:

Do as per the above trick.

1.place 2 as the right digit.

2. Add 1st 2 digit i.e; 5+2=7

3. Then add another 2 digit 5+6=11

4 combine them to get answer

            ____2

            ___7

          11

          6

____________

7172

I KNOW YOU HAVE DOUBTS.SO ASK ME IN COMMENT BOX. DON'T HESITATE.

let's move to the third question.

Algorithm:

1.place 3 as right digit

2. Here no. Of 1 is 3.so we do 3 digit addition maximally.But starts from 2 digit addition.

3.add 0+3=3

4.add 2+0+3=5

5.add 2+0=2

6. Place the 2 as left digit.

So answer is 22533.

I REPEAT IF YOU HAVE ANY DOUBT PLEASE COMMENT ME.

Lets Take another Example.

201432×111

Algorithm:

The (2) in the units place of the multiplicand is written as the units digit of the answer

• We move to the left and add (2 + 3) and write 5

• We move to the left and add (2 + 3 + 4) and write 9

• We move to the left and add (3 + 4 + 1) and write 8

• We move to the left and add (4 + 1 + 0) and write 5

• We move to the left and add (1 + 0 + 2) and write 3

• We move to the left and add (0 + 2) and write 2

• We move to the left and write the single digit (2) in the answer.

Ex.210432×1111

AND the last two questions are H.W. For You.

Multiplication of Numbers With a Series of 9's

Everyone know that 9 is the biggest number among all one digit numbers.

If i asked You to do the following exercise in just 5seconds.Can you do it?

Can Notice That It is not one type.It is of 3 types.

1.No.of Digits in 1st Number is equal to no.of 9's

2.No.Of Digits in 1st Number is less than no. Of 9's

3.No. of digits in 1st Number is greater than no. Of 9's

Algorithm:

For Type(1):(Multiply a Number with an equal number of nines)

Ex: 654×999

1. Subtract 1 From the 654 and write as left part of the answer.

2.Now subtract the left Part of the answer from 999 and place as right part of the answer.

For Type(2):(Multiply a Number with higher number of nines)

Ex:45×999

1.Make eual digits as per the  numer of nines.

2.Do as before explained.

And Finally The last case is 

Type(3)(Multiply a Number With a lower number of nines)

1.Instead of Multiplying 99 we can do it as (100-1)

2.Subtract that number from the result.

Hope You will Remember it.

Squaring Of Numbers Between 50 & 60

I think you will not miss this trick.I had explain you a trick for squaring numbers but this trick help you very much.

This tricks only works for numbers between 50 and 60.But I want to say you that if you really like this tricks and read all this blogs carefully then you can find same trick with all numbers but you have to do some little changes.

Okay,Lets start.

In the above questions i will do only one and the other will remain for you.

Note: You should take 25 as your reference in all cases.

Algorithm:

1.Add 25 to the digit in unit place and put it as left part of the answer.

2.square the digit of unit place and put it as right part of answer.

(All are graphically mentioned)

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A Perfect Square

I think nobody knows these sillythings.

Did you ever notice that you are much slower in calculations.😥

Then not to worry i will teach you how to fast in calculation.

If i asked you to square the number 58 in just 2second.

I will give a trick to make this simple.

Before we go to the formula you must lookout the relationship.

I found this pattern astonishing. Next I tried numbers that add to 26 and got similar results. First I worked out 13²=169,

then computed 12 ×14 =168, 11×15 = 165, 10× 16 =160.

so by this rule i got that if you have to square a number take a nearest number that end up with '0' (to do more faster calculation).

Take another number which is also same difference of the before two numbers but take the opposite side.

Ex.if you 1st take in greater side the you have to choose in smaller side.

So here we Have to Calculate 13²

We simply do

1.16×10=160

2.3²=9

3.160+9

You can also do it as (14×12)+1²

0r (11×15)+2² or etc.

This is the task for you 

1. 98²=?

2.67²=?

3.85²=?

And also share and visit the site for more new tricks at. Math Tricks

A Quick Multiplication

If i asked You To solve 87×83 in 2second.

Can you do it??

If yes,Great

If no then alright i will teach you.

Let Me explain!

This Trick has Some merits and some demerits.

NOTE:

1.This Trick Only works for 2×2 Multiplication 

2.The addition of the right of the two numbers should be 10.

3.The left digit of the two number should be same.

How about the square of 85?Since8÷9=72, we immediately get 85×85= 7225.

We can use a similar trick when multiplying two-digit numbers with the same first digit, and second digits that sum to 10.

The answer begins the same way that it did before (the first digit multiplied by the next higher digit), followed by the prod-

uct of the second digits. For example, let’s try 83×87. (Both

numbers begin with 8, and the last digits sum to 3+7 =10.)

Since 8×9=72, and 3×7 =21, the answer is 7221.

😊 Now Its your Turn

Do it as described above

1.57×53=?

2.46×44=?

3.91×99=?