# Long Division

As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend one at a time starting with the highest place.

Division by One-Digit Divisor

1. Divide 27 by 9

Solution:

Let us divide.

 Step I: Write 27 inside the bracket and 9 on the left side of the bracket.Step II: Start division from left to right, that is, divide 2 by 9. Since, we cannot divide 2 by 9 so, we will divide 27 by 9.Step III: Recall the table of 9.9 × 3 = 27Now, write 3 in the quotient and subtract 27 from 27. The result is 0.Thus, 27 ÷ 9 = 3

2. Divide 92 by 4

Solution:

Let us divide.

 Step I: Write 92 inside the bracket and 4 on the left side of the bracket.Step II: Start division from left to right, that is, divide 9 tens by 4. 4 × 2 = 84 × 3 = 1212 tens is bigger than 9 tens, so we take 4 × 2 = 8 tens.Step III: Write 2 in the quotient.Step IV: Subtract 8 from 9 and get 1 as remainder.Step V: Bring down 2 from ones place and write it to the right of 1. 12 is the new dividend.Step VI: Write 3 in the quotient and subtract 12 from 12. The result is 0. Thus, 92÷4 = 23

3. Find the quotient and remainder of 649 ÷ 9.

Solution:

 Step I: We start dividing the hundreds first. Since 6 hundreds cannot be divided into 9 groups of hundreds, the quotient at hundreds column is zero.Step II: 6 Hundreds are now changed into 60 tens and added to 4 tens, making 64 tens.Step III: 64 tens give 9 groups of 7 tens each and 1 ten is left over.Step IV: 1 ten give 10 ones, 10 ones + 9 ones = 19 onesStep V: 19 ones can be put into 2 groups of 9 and 1 one is left over. q = 72; r = 1

Division by Two-Digit Divisors

4. Divide 2698 by 21.

Solution:

Recall the process of long division.

 Step I: 2 thousands cannot be divided into 21 groups of thousand. So, 0 is placed as quotient in the thousands column.Step II: 2 thousands give 20 hundreds.20 hundreds + 6 hundreds give 26 hundreds. 26 hundreds make 1 group of 21 hundreds. 5 hundreds are left.Step III: 5 hundreds give 50 tens. q = 128; r = 10

So, 50 tens + 9 tens = 59 tens

59 tens are to be divided into 21 groups of tens

59 tens ÷ 21 makes 2 groups with 17 tens left.

2 is placed in the quotient in the tens column.

Step IV: 17 tens = 170 ones

170 ones + 8 ones = 178 ones

178 ones ÷ 21 makes 8 groups with 10 ones left.

Thus, in division of 2,698 by 21, we get 128 as quotient and 10 as remainder.

Word Problems on Long Division:

To solve any word problem, we need to read each word carefully and select numbers carefully from the question to solve it.

5. If 60 cookies to be put in 5 packets, how many cookies will be packed in one packet?

 Solution:Number of cookies = 60 cookiesEqually distributed in 5 packetsNumber of cookies in one packet = 60 ÷ 5

Thus, 12 cookies will be packed in one packet.

Questions and Answers on Long Division:

I. Divide and find the quotient:

(i) 85 ÷ 5 =

(ii) 54 ÷ 3 =

(iii) 63 ÷ 7 =

(iv) 60 ÷ 3 =

(v) 42 ÷6 =

(vi) 32 ÷ 8 =

(vii) 88 ÷ 8 =

(viii) 69 ÷ 3 =

(ix) 48 ÷ 3 =

(x) 42 ÷ 6 =

(xi) 68 ÷ 4 =

(xii) 96 ÷ 6 =

I. (i) 17

(ii) 18

(iii) 9

(iv) 20

(v) 7

(vi) 4

(vii) 11

(viii) 23

(ix) 16

(x) 7

(xi) 17

(xii) 19

II. Solve the given word problems on long division.

1. Shelly has 75 pencils. She shares them between her 5 friends. How many pencils will each of her friend get?

2. In class III, there are total 70 children. If there are 5 sections in class III, how many children are there in each section?

3. There are 68 birds in a zoo in 4 cages. How many birds are there in each cage?

4. Jack, the clown has 99 balloons which he needs to share between 9 children at the fair. How many balloons does each child get?

5. Nancy has 96 pieces of candy. She has 8 bags. She wants to put the same amount of candies in each bag. How many will she put in each bag?

6. Mike organised 24 chairs in 4 rows for a party. How many chairs are there in each row?

7. You have 60 gum balls that you need to share equally in five containers. How many gum balls will be in each container?

8. There are 96 books on the shelf. If the books are to be shared equally amongst 4 table groups in the class, how many books will be there on each table?

II. 1. Shelly has 75 pencils. She shares them between her 5 friends. How many pencils will each of her friend get?

2. In class III, there are total 70 children. If there are 5 sections in class III, how many children are there in each section?

3. There are 68 birds in a zoo in 4 cages. How many birds are there in each cage?

4. Jack, the clown has 99 balloons which he needs to share between 9 children at the fair. How many balloons does each child get?

5. Nancy has 96 pieces of candy. She has 8 bags. She wants to put the same amount of candies in each bag. How many will she put in each bag?

6. Mike organised 24 chairs in 4 rows for a party. How many chairs are there in each row?

7. You have 60 gum balls that you need to share equally in five containers. How many gum balls will be in each container?

8. There are 96 books on the shelf. If the books are to be shared equally amongst 4 table groups in the class, how many books will be there on each table?

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