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.