Addition and Subtraction
Category : 2nd Class
LEARNING OBJECTIVES
This lesson will help you to:—
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
For example 3 + 0 = 3
3 + (2 + 5) = (3 + 2) + 5 = 10
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
\begin{align} & \underline{\begin{matrix} Tens \\ 3 \\ 4 \\ \end{matrix}\begin{matrix} Ones \\ 9 \\ 6 \\ \end{matrix}}\to \\ & \,\,\,\,\,\,\,\,\,\,\,\,\, \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\to \\ \end{align} 
First, add 9 + 6 = 15 Write 5 in ones and carry over 1 to the tens place
Now, add 1 + 3 + 4 = 8

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
METHODS OF SUBTRACTION
(a) Subtraction without regrouping:
For example:
For, 3714
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 fingertips for 1diait 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.
\[\frac{+\,\begin{matrix}
T & O \\
2 & 3 \\
3 & 1 \\
\end{matrix}}{5\,\,\,\,4=54}\]
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