# Multiplication

Some of the methods are given below:

# Base Method

In this method of multiplication, we use a number as a base, like 10, 50, 100 etc. We should try to assume the base that is closer to both the numbers.Example-1

105 Ã— 107

Solution

Both the numbers are close to 100, so let us assume 100 as the base. We will now find the deficit/surplus from the base.

Base = 100, Surplus = 5 and 7

Right part (after slash) is the product of the surplus. Since base = 100 and surplus are 5 and 7, so product would be 5 Ã— 7 = 35.

Example-2

97 Ã— 102

Solution

97 Ã— 102

# Place value Method

In this method of multiplication, every digit is assigned a place value and we do the multiplication by equating the place values of multiplicands with the place value of the product.Example

Solution

Conventionally, the unit digit is assigned a place value of 0, tens place digit is assigned a place value of 1, hundreds place digit is assigned a place value of 2, thousands place digits is assigned a place value of 4 and so on.

Now, this multiplication is a two-step process:

# Step 1

Add the place values of digits of the numbers given (1254 Ã— 3321) to obtain the place value of the digits of the product.

For example, using the place values of the multiplicands i.e., using 0, 1, 2 and 3 of the number 1254 and the same place values 0, 1, 2 and 3 of the other multiplicand 3321, we can get 0 place value in the product in just one way i.e., adding 0 and 0.

Place value 1 in the product can be obtained in two ways:

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Place value 2 can be obtained in three ways:

Place value 3 can be obtained in four ways:

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Place value 4 can be obtained in three ways:

Place value 5 can be obtained in two ways:

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Place value 6 can be obtained in one way:

And this is the maximum place value that can be obtained.

# Step 2

Now multiply the corresponding numbers one by one.â€‹

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And so on, we can find the product = 4164534

This method is most useful in case of multiplications of 2 digits Ã— 2 digits or 2 digits Ã— 3 digits or 3 digits Ã— 3 digits multiplication.

Example

ab Ã— cd

Solution

Similarly, we can have a proper mechanism for multiplication of 2 digits Ã— 3 digits or 3 digits Ã— 3 digits using the above given place value method.