Division
Category : 2nd Class
LEARNING OBJECTIVES
This lesson will help you to:—
QUICK CONCEPT REVIEW
DIVISION
Division means equal sharing or making groups of equal things.
Let us understand with the help of an example.
Maria has 4 rabbits. She has 8 carrots that she wants to distribute equally among them. How many carrots will each rabbit get?
This can be solved by using Division
First Maria will give one carrot to each rabbit
Step 1
Then she finds that she still has some carrots. Now she gives one more carrot to each rabbit.
Step 2
There is no more carrot left now. Each rabbit gets 2 carrots.
So, here Maria equally divides 8 carrots among 4 rabbits.
Real Life Examples
Properties of Division
When we divide a number other than 0 by 1, we get the number itself.
For example \[\text{8}\div \text{1}=\text{8}\]
\[\text{1}0\text{ }\div \text{ 1 }=\text{ 1}0\]
When we divide zero by a number we get '0' as answer.
For example: \[0\div 6=0\]
\[0\div 13=0\]
When we divide a number other than zero by the number itself we get 1 as answer.
For example: \[10\div 10=1\]
\[13\div 13=1\]
\[0\div 0=0\]
Historical Preview
Methods of Division
1. Short division with remainder method:
Divide 30 by 8.
It can also be written as \[30\div 8\]
Step 1: Arrange the numbers in the following manner \[8\overline{\left){30}\right.}\]
Step 2: We divide from left
\[\text{8 }\times \text{ 3 }=\text{ 24}\]which is less than 30
\[\text{8 }\times \text{ 4 }=\text{ 32}\]which is more than 30
we take 3 as quotient
\[\text{8 }\times \text{ 3 }=\text{ 24}\]
\[\text{3}0\text{ }-\text{ 24 }=\text{ 6}\]
Thus we have
2. Division with no remainder:
Let us consider an example where no remainder is left on division.
Divide93 by 3 or \[93\div 3\]
Now, consider division of 930 by 3.
Here the zero left in the dividend will shift to the quotient.
3. Long Division Method:
Divide 93 by 4 using long division method
Step 1: Arrange the numbers in the following manner.
\[4\overline{\left){93}\right.}\]
Step 2: We divide from left.
\[\text{4}\times \text{2}=\text{8}\]which is less than 9 and
\[\text{4}\times \text{3}=\text{12}\]greater than 9
We take 2 as quotient
\[\text{4}\times \text{2}=\text{8}\]
\[\text{9}-\text{8}=\text{1}\]
Step 3: We see\[\text{4}\times \text{3}=\text{12}\]which is less than 13 and\[\text{4 }\times \text{ 4 }=\text{ 16}\]which is more than 13.
Basic term used in division
Relation between Dividend, Divisor. Quotient and Remainder:
\[\text{Dividend }=\text{ }\left( \text{Quotient }\times \text{ Divisor} \right)\text{ }+\text{ Remainder}\]
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