2nd Class Mathematics Addition and Subtraction Addition and Subtraction

LEARNING OBJECTIVES

This lesson will help you to:—

• understand the concept of addition and subtraction.
• add and subtract 2-digit numbers.
• add and subtract with or without regrouping.

QUICK CONCEPT REVIEW

ADDITIONS

Suppose you have 3 apples and your friend gives you 4 more apples. How many apples will you have?

Here, you need to learn addition.

3 + 4 = 7

So, you will have 7 apples with you.

Let us learn some methods to do addition.

Also, you should know that '+' sign is used as a symbol of addition.

PROPERTIES OF ADDITION

• Adding 0 to a number gives number itself.

For example 3 + 0 = 3

• Addition is an associative property.

3 + (2 + 5) = (3 + 2) + 5 = 10

• Order of addition does not matter, e.g.

    12 + 13 = 13 + 12

METHODS OF ADDITION

(a) Putting together                            

            4                  +                       3                         =              7

Here, we combine the two collections and find the total.                                  

Let us take another example

                             3       +                   2      +     1    =                 6                 

(b) Addition without regrouping

Examples:

1. Add 2 + 6 + 7

Here, first you have to add 2 and 6. Then finally add 7 to the sum.

2. Add 23 + 12

\begin{align}

  & Arrange\,the\,\,\,\,\,\,23\xrightarrow{{}}\,tens+\,\,\,ones \\

 & number\,in\,\,\,\,\,\,\,\,\,\,\,12\xrightarrow{{}}\underline{\,ten\,\,\,\,\,\,+\,\,\,ones} \\

 & column\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ten\,\,\,\,\,\,\,\,\,\,\,\,ones \\

 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Add\,\,\,\,\,\,\,\,\,\,\,\,Add \\

 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,tens\,\,\,\,\,\,\,\,\,\,\,\,\,ones \\

\end{align}

 You can write 16 and 27 in columns.

(c) Addition with regrouping

Example:

Add 16 + 27

\begin{align}

  & \,\,\,\,16\xrightarrow{{}}\,\,\,tens\,\,\,+\,\,\,ones \\

 & +\,27\xrightarrow{{}}\underline{\,ten\,\,\,\,\,\,+\,\,\,ones} \\

 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ten\,\,\,\,\,\,\,\,\,\,\,\,ones \\

\end{align}

13 can be written as 1 ten and 3 ones.

So, 3 tens + (1 ten + 3 ones)

                = (3 tens + 1 ten) + 3 ones.

                = 4 tens + 3 ones

                =43

Hence, the sum 16 + 27 = 43

(d) Addition with carry over method

Example:

Add 39+46

So, the sum of 39 and 46 is 85.

SUBTRACTION

Assume you have 5 chocolates, and 2 chocolates are taken away. How many chocolates will you have?

This problem can be solved by using subtraction.

\[\text{5}~~~~~~~~~~~~~~~~~~~-~~~~\text{2}~~~~~~~=~~~~\text{3}\]

PROPERTIES OF SUBTRACTION

• When zero is subtracted from a number, we get number itself.
• \[3-0=3\]
• Order of numbers affects the subtraction.
• \[3-2\ne 2-3\]
• Sign of subtraction is'-'.

METHODS OF SUBTRACTION

(a) Subtraction without regrouping:

For example:

For, 37-14

First write 37 and 14 in columns.

step (1) subtract ones

step (2) subtract tens

\begin{align}

  & \,\,\,\,37\xrightarrow{{}}\,\,tens\,\,\,ones \\

 & -14\xrightarrow{{}}\underline{\,\,tens\,\,\,ones} \\

 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,tens\,\,\,\,ones=23 \\

\end{align}

(b) Subtraction with regrouping (Carry over method):

For example:

For, 36 -19

First write 36 and 19 in columns

Since 6 < 9. we have to borrow 1 ten from 3 tens of 36 3 tens becomes 2 tens. 6 ones becomes 16.

\begin{align}

  & \,\,\,\,36\xrightarrow{{}}\,\,tens+\,\,\,ones\to 2\,\,ten\,\,\,\,\,16\,\,ones \\

 & -19\xrightarrow{{}}\underline{\,\,ten\,\,\,\,\,+\,ones\to }\underline{\,\,1\,\,\,ten\,\,\,\,\,9\,\,\,\,ones} \\

 & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,tens\,+\,ones \\

\end{align}

Thus, 36 - 19 = 17

Let us consider another example:

Subtract 19 from 47.

Arrange in columns

Here, 7 < 9, we borrow 1 tens from 4 tens of

47: 7 ones of 47 becomes 17.

\[\underline{\begin{align}
  & Tens\,\,Ones \\
 & \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,7 \\
 & -1\,\,\,\,\,\,\,\,\,\,9 \\
\end{align}}\]

\[\frac{\begin{align}
  & Tens\,\,Ones \\
 & 3\,\,\,\,\,\,\,\,\,\,17\,\, \\
 & -1\,\,\,\,\,\,\,\,\,\,\,\,\,9 \\
\end{align}}{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8}\]

MENTAL ARITHMETIC

If you have not been given any pen, pencil or paper to do addition or subtraction than how will you do the calculation?

You can do calculations on finger-tips for 1-diait numbers,

Examples:

Adding 3 and 4

Count fingers starting after 3. It will be 4 then 5 then 6 and then 7. So, the answer is 7.

\[\text{3 }+\text{ 4 }=\text{ 7}\]

We can also do addition by following ways using our finger tips.

(a) Add 10 and 30.

You can do addition by skip counting on fingers starting from 10.

\[\frac{+\,\begin{matrix}
   T & O  \\
   1 & 0  \\
   3 & 0  \\
\end{matrix}}{\,\,4\,\,\,\,\,\,\,0=40}\]

(b) Add 23 + 31

First add ones digit of 31 which is 1 to 23 It will give 24 and then do skip counting three times of tens digit.               

\[\frac{+\,\begin{matrix}
   T & O  \\
   2 & 3  \\
   3 & 1  \\
\end{matrix}}{5\,\,\,\,4=54}\]

Historical Preview

• Addition sign (+) was invented by Michael stiple in 1544.
• A few seventh century books used two dots or three dots for subtraction.

Real Life Examples

• When you count your money you add one by one.
• We use addition and subtraction when we shop many things, give payment and receive balance.