Suppose you have 21 chocolates with you. You have six friends. You want to distribute the chocolates equally amongst yourselves. How do you do that ?
First, you give a chocolate to each of your friends and keep one for your self. How many chocolates are distributed ? 6 + 1 = 7. Out of 21, 7 chocolates are distributed. How many are remaining ? 21 - 7 = 14.
Now you give one more chocolate to each of your friends and again keep one for your self. This time how many are given ? again 6 + 1 = 7. How many remain ? 14 - 7 = 7.
For the third time you distribute one chocolate to each of your friends and keep one for your self. This time also you distributed 6 + 1 = 7. How many remain ? 7 - 7 = 0.
We can subtract 7 from 21 three times. or 7 goes three times in 21.
How many chocolates does each one of you get ?
Since you have distributed three times, each one of you gets 3 chocolates.
Now, we can say, when 21 chocolates are distributed equally among 7 friends, each one gets 3 chocolates.
That means, when 21 is divided by 7, 3 is obtained. We write this as 21 ÷ 7 = 3.
The above example is an example of Division as repeated subtraction.
Instead of distributing three times, you want to give at a time, the equal share of chocolates to each one of you by packing the chocolates.
i.e. you want to make 7 packs from the 21 chocolates. How many chocolates are to be put in each pack ?
You need to know before hand, that 3 chocolates are to be put in each pack. That means you need to know 21 ÷ 7 = 3.
Let us see one more example.
Example 2 : Division as repeated subtraction
Suppose you have 20 pencils. You have to make packs of five pencils each. How many packets can you make ?
See the difference between this problem and the previous one. There we know the number of packs and the number of items in each pack are to be known. Here, we know the number of items in each pack and the number of packs are to be known.
How do you solve this problem ?
First you seperate a set of 5 pencils from the 20 pencils and make that set of 5 as a pack. Then how many pencils remain ? 20 - 5 = 15.
Then, you seperate another set of 5 pencils from this 15 and make it as another pack.Then how many pencils remain ? 15 - 5 = 10.
For the third time, you seperate another set of 5 pencils from this 10 and make it as a pack.Then how many pencils remain ? 10 - 5 = 5.
You make this remaining 5 as a fourth pack.
Thus, you make 4 packs of 5 pencils each from the given 20 pencils.
We can say this as : we can subtract 5 from 20 four times. Or 5 goes four times in 20. That means we get 4 when 20 is divided by 5. We write this operation as 20 ÷ 5 = 4.
If you know, 20 ÷ 5 = 4, you can answer that you can make 4 packs of 5 pencils each from the given 20 pencils without actually making the sets.
You have seen the concept of division as sharing equally every time in Example 1 and as making sets in Example 2.
Exercise on Division Word problems
How many packs of 2 biscuits can we make from 10 biscuits ?
How many times can we subtract 5 from 15 ?
How many times does 4 go in 16 ?
12 apples are distributed among 4 persons. How many apples does each person get ?
How many pairs can we make out of 12 socks ?
Each shelf can accomodate 5 books. How many shelves are required to put 25 books.
6 students can sit on a bench. How many benches are required for 30 students ?
24 students have to stand in 8 rows. How many students have to stand in each row.
We have to make 6 parcels out of 18 items. How many items are to be put in each parcel ?
To how many students can you distribute 18 chocolates, if each student has to get 2 chocolates ?
For Answers see at the bottom of the page.
Relation between multiplication and division
In both examples 1 and 2, we have seen the concept of division as repeated subtraction.
We have already seen the concept of
Multiplication as repeated addition.
Look at the example 1, above. How many chocolates are there with all the seven friends ? Each one has 3 chocolates. So all of them have 3 + 3 + 3 + .....7 times = 7 times 3 = 7 x 3 = 21.
We already have 21 ÷ 7 = 3.
See the link between the two statements. If 21 ÷ 7 = 3, then 7 x 3 = 21. Or if 7 x 3 = 21, then 21 ÷ 7 = 3.
So finding 21 ÷ 7 is nothing but finding a number which when multiplied by 7 gives 21. Or how many times 7 gives 21.
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