2nd Class Mathematics Multiplication Multiplication

LEARNING OBJECTIVES

This lesson will help you to:—

• learn about groups.
• know about repeated addition.
• know about multiplication as repeated addition.
• learn multiplication of one-digit and two-digit
• numbers

QUICK CONCEPT REVIEW

MULTIPLICATION

What is a Group?

Let us understand with the help of examples.

There are 5 pencils in this box. We can say this is group of 5 pencils.

Now consider two boxes of pencils.

These are 2 groups of 5 pencils each. Equal groups

Look at these three groups of birds.

There is an equal number of birds in each group i.e., 3.

To find the total number of birds, the same number is added again and again. This repeated addition is called multiplication.                           

Amazing Facts

Any two number multiplied in any order or sequence gives the same answer.

For Example:      \[10\times 2=20\]and

                                \[2\times 10=20\]

PROPERTIES OF MULTIPLICATION

• 'x' is the symbol of multiplication.
• When we multiply the number, the answer is called the product.

\[4\times 2=8\]

In this example, the number 8 is the product.

• When a number is multiplied by 0 or 0 is multiplied by a number, then the product is always '0'.                              

        \[0\times 1='0'1\times 0='0'\]

Real Life Examples

If you want to buy 10 dozens of banana then you can calculate the number of banana as well as its price by the method of multiplication.

For Example.

1 dozen = 12 bananas

10 dozen = \[12\times 10=120\]bananas

If cost of 1 dozen banana is Rs. 10

Then const of 10 banana can be calculated as:

\[10\times Rs.10=Rs.100\]

Let us discuss some examples:                

1. Look at the 3 lots of 5 pencils    

Each lot has 5 pencils,                        

Therefore, 5 + 5 + 5 = 15.                     

or '3 x 5 = 15                                  

or "3 multiplied by 5 is 15'.                    

or '3 times 5 is 15.'                        

2. How many legs will 5 horses have?

Each horse has 4 legs. So, 5 horses will have  

\[\text{4}+\text{4}+\text{4}+\text{4}+\text{4}=\text{ 2}0\text{ Legs}.\]

In this 4 is repeatedly added 5 times.

or, \[\text{4 }\times \text{ 5 }=\text{ 2}0\]

Do you know?

• Multiplication is an expanded from of addition. We need it when we want to add several things of the same value.

Now, you must be thinking that how to do big repeated additions. It will be very difficult.

For that, you can use multiplication tables which are made for two times, three time____ upto ten times.

Let us write these multiplication facts in a table.

Following are multiplication tables of 3 and 5.

MULTIPLICATION OF COLUMN FORM

1. One - digit multiplied by one - digit

\[3\times 4=12\]                                                                                                                                                                                              \[2\times 6=12\]

2. Two - digits multiplied by one - digit

Let us take an example

\[\text{12}\times \text{3}=\text{36}\]

First multiply 2 ones of 12 with 3, \[\text{2}\times \text{3}=\text{6}\].

Then multiply 1 tens of 12 with 3, \[\text{1}\times \text{3}=\text{3}\]

hence, \[\text{12 }\times \text{ 3 }=\text{ 36}\].

Let us now consider some examples of multiplication involving carry over.

For example:

\[\text{18}\times \text{5}=\text{9}0\]

Here, 4 is carried over from ones place and this is added in the product of \[\text{1}\times \text{5}=\text{5}\] and \[\text{5}+\text{4}=\text{9}\]

hence, \[\text{18}\times \text{5}=\text{9}0\].

SOME IMPORTANT CONCEPT

1. Do you know that\[~\text{1}0\times \text{1}=\text{1}0\].

Which can also be written as\[~\text{2}\times \text{5}=\text{1}0\]

or\[~\text{5}\times \text{2}=\text{1}0\].

Examples:

1. 24 can be written as \[\Rightarrow \]

\[\text{l}\times \text{24}=\text{2}\times \text{12 }=\text{3}\times \text{8}=\text{4}\times \text{6}\]

2. 18 can be written as \[\Rightarrow \]

\[\text{l}\times \text{18 }=\text{2}\times \text{9}=\text{3}\times \text{6}=\text{9}\times \text{2}\]

1. If you want to multiply any number with 10, just write '0' after that number.

Example: \[~\text{4}\times \text{1}0=\text{4}0\].

Historical preview

• The modern method of multiplication based on the Hindu-Arabic numeral system was first described by Brahmagupta.