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Class III - Maths: Division
One Word Answer Questions:
Q) Write the quotient for 7246 / 1 = ___?
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Q) Divide 575 by 5?
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Q) Complete the following 8 * 5 = 40 so,40 / 8 =___ and 40 / 5 =___?
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Q) find Solve and write the quotient for 63 / 9 = __?
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Q) Fill I the blanks 5320 / 5320 = __?
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Short Answer Questions:
Q) How many sevens are there in 25? Let us substract?
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Q) Divide 38 by 6?
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Q) Divide and find the quotient and remainder for 36 / 8?
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Q) Divide each of the following by 10 for 875?
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Q) solve the following by repeated substraction for 45 / 9?
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Long Answer Questions:
Q) Write about rules of division?
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Q) 9 tickets were put into one envelope. How many envelopes are needed to put 2800 ticketsHow many tickets will be left?
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Q) Divide 5306 by 5?
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Q) 1032 eggs are to be placed equally in 6 trays. Find the number of eggs each tray?
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Division

You have learnt about division in the previous class. You know that division means equal sharing and equal grouping. Here, we have to find either the number of shares or the number to be put in each group or share.

Example:-

→ oranges are to be kept equally in 4 baskets. So, we put 20 ÷ 4 oranges in each basket. We put 5 oranges in each basket. This is called equal sharing.

20 ÷ 4=5
20 = dividend
4= divisor
5=quotient

•Division is also called repeated subtraction. How many fives are there in 10?

            10                     
            -5    1    (first five)                   
             5						  
            -5    2    (second five)
             0                        

•We can subtract 5 from 10, two times.So, there are 2 fives in 10.This is the same as 10÷5=3 2 in 15.This is the same as 10÷5=2

Rules of Division

While dividing numbers, we follow certain rules.

Dividing by 1

When we divide any number by 1, it gives the quotient as the number itself.

So,    8 ÷1=8                         25 ÷1=25
                                    
    376 ÷1=376                     4934 ÷1=4956

Dividing 0 by a number
When we divide zero by any number, it gives the quotient as 0.
So,         0 ÷5=0               0 ÷25=0
Dividing a number by itself

Let us find out how many sixes there are in 6. We do this by repeated subtraction ( which is division).

		          6
			- 6 
			  0

Since we can subtract a number from itself only once, we can say that any number divided by itself gives the quotient as 1.
So,          8 ÷8=1   72 ÷72=1
THE REMAINDER

What is a remainder? Let us see a few examples of division with remainder.

1. There are 12 apples. One plate can hold 5 apples. How many plates are needed so that each plate holds and equal number of apples? Two plates.

You can see that 2 apples are left over. The number of left over things is called the remainder.

2.How many sevens are there in 25? Let us subtract.
                            25
                            -7  → 1
                            18                                  
                            -7  → 2                           
                            11
                            -7  →  3
                             4  → remainder 

•We can subtract 7 from 25 repeatedly 3 times, but 4 is left over. So, 4 is the remainder.

•Sometimes when we divide a number by another number, we get a remainder.

Long Division

•Let us work out division in another way. This is called the long division. We can write 56÷7=8 as given on the next page.

T   O

8 → Quotient

Divisor →7 ` sqrt(5      6)` → Dividend

Example:
Divide 66 by 8.

Solution: You know that 8×8=64, which is less than 66.So, write 8 in the quotient and subtract 64 from 66.

T   O

8

8 ` sqrt(6      6)`

-6   4

2

CHECKING DIVISION

We can check every long division question. If Dividend =( Divisor × Quotient)+ Remainder, then the division problem has been correctly solved. In the above division sum, let us check this out.
Dividend =66  Divisor =8  	Quotient =8  Remainder= 2

Verification:

		Divisor × Quotient + Remainder
		   = 8×8+2=66
		   = Dividend (verified).

GETTING 2-DIGIT QUOTIENTS

So far we have been dividing numbers in which the quotients have been single digit numbers. We may get 2-digit quotients on dividing bigger numbers, they are not given as products in the tables we have learnt. Let us now learn how to divide bigger numbers.

Example:
Divide 96÷8.
Solution:

Step 1: Write the dividend and divisor as shown.

T   O

8`sqrt(9    6)`

Step 2: Take the first digit from the left of the dividend, 9. From the multiplication table of 8, you know that 8×1 =8, which is less than 9. Write 1 in the quotient at the tens place and product 8 under 9 and subtract. Here, 1 tens is the remainder.

T   O

1

8 ` sqrt(9      6)`

-8   

1

Step 3: Write the next digit 6 at the right side of 1 in the ones place. You have 16 ones. Find out how many fives give 16.

T   O

1  2

8 ` sqrt(9      6)`

-8    

1   6      8×2=16.

1   6

0   

Write 2 in the ones place in the quotient and the product 16 under 16 and subtract.

DIVIDING 3-DIGIT AND 4-DIGIT NUMBERS

  • When the dividend is a 3 digit number, we may get quotients which are 2 digit or 3 digit numbers.
  • Example: Divide 162 and 6 and verify the answer.

    Solution:
  • The steps for dividing a 3 digit number are the same as those for dividing a 2 digit number by the long division method.
  • Step 1: We start division from the place of highest value which is the hundreds place. Since we cannot divide 1 hundreds by 6, we regroup and consider 1 hundreds and 6 tens = 16 tens.
  • 16 tens ÷6 = 2 tens and remainder is 4. Write 2 in the tens place in the quotient.
  • Step 2: Bring down 2 alongside the 4 tens (remainder). So, new dividend is 42.
  • Divide 42 ones by 6.

    42÷ 5= 7 ones. Write 7 in the ones place in the quotient. Here, the remainder is 0.

    H      T      O

    2      7

    6 `sqrt(1     6      2)`

    -1   2    

    4   2

    - 4   2

    0   0

    Answer: Quotient =27 and remainder =0.
    Divisor × Quotient + Remainder
         =8 × 28 + 0
         = 224 = Dividend
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