As we know, division consists in dividing a certain value or amount into groups of equal values. With long division, the values â€‹â€‹are divided individually at each digit (thousands, hundreds, tens, ones), starting with the highest digit.
Division by a single-digit divisor
1. Divide 27 by 9
Solution:
Let’s share.
Step I: Write 27 in the bracket and 9 on the left side of the bracket. Step II: Start by dividing from left to right i.e. divide 2 by 9. Since we can’t divide 2 by 9, we are going to divide 27 by 9. Step III: Remember the table from 9. 9 × 3 = 27 Now write 3 in the quotient and subtract 27 from 27. The result is 0. So 27 ÷ 9 = 3 |
2. Divide 92 by 4
Solution:
Let’s share.
Step I: Write 92 in the bracket and 4 on the left side of the bracket. Step II: Start by dividing from left to right, that is, divide 9 tens by 4. 4 × 2 = 8 4 × 3 = 12 12 tens are greater than 9 tens, so let’s take 4 × 2 = 8 tens. Step III: Write 2 in the quotient. Step IV: Subtract 8 from 9 and get 1 as the remainder. Step V: Drag 2 down from your 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. So 92 ÷ 4 = 23 |
3. Find the quotient and the remainder of 649 ÷ 9.
Solution:
Step I: We’ll start dividing the hundreds first. Since 6 hundreds cannot be divided into 9 hundreds groups, the quotient in the hundreds column is zero. Step II: 6 hundreds are now converted to 60 tens and added to 4 tens, making 64 tens. Step III: 64 tens result in 9 groups of 7 tens each and 1 tens is left over. Step IV: 1 Ten equals 10 ones, 10 ones + 9 ones = 19 ones Step V: 19 ones can be divided into 2 groups of 9 and 1 of them is left over. |
q = 72; r = 1 |
Division by two-digit divisors
4th Divide 2698 by 21.
Solution:
Do you remember the process of long division.
Step I: 2 thousand cannot be divided into groups of 21 thousand. So 0 is put in the thousands column as a quotient. Step II: 2 thousand makes 20 hundred. 20 hundreds + 6 hundreds equals 26 hundreds. 26 hundreds make a group of 21 hundreds. 5 hundred are left. Step III: 5 hundreds equals 50 tens. |
q = 128; r = 10 |
So, 50 tens + 9 tens = 59 tens
59 tens are divided into 21 groups of ten
59 tens ÷ 21 results in 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 makes 21 results in 8 groups with 10 ones left.
If we divide 2,698 by 21, we get 128 as the quotient and 10 as the remainder.
Word problems with long division:
To solve any word problem, we need to carefully read each word and carefully choose numbers from the question to solve.
5. If 60 biscuits are to be packed in 5 packages, how many biscuits are to be packed in one package?
Solution: Number of cookies = 60 cookies Distributed equally in 5 packets Number of cookies in a package = 60 ÷ 5 |
Thus, 12 biscuits are packed in one package.
Questions and answers about the 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 =
Reply:
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 in the long division.
1. Shelly has 75 pencils. She shares it between her 5 friends. How many pencils does each of her friends get?
2. In class III there are a total of 70 children. If there are 5 sections in Class III, how many children are there in each section?
3. 68 birds live in 4 cages in a zoo. How many birds are in each cage?
4. Jack the clown has 99 balloons that he has to share between 9 children at the fair. How many balloons does each child get?
5. Nancy has 96 candies. It has 8 pockets. She wants to put the same amount of candy in each bag. How many will she put in each pocket?
6. Mike organized 24 chairs in 4 rows for a party. How many chairs are there in each row?
7. You have 60 gum balls that you must divide equally into five containers. How many gum balls are in each container?
8. There are 96 books on the shelf. If the books are to be evenly distributed over 4 groups of tables in the class, how many books will there be on each table?
Reply:
II. 1. Shelly has 75 pencils. She shares it between her 5 friends. How many pencils does each of her friends get?
2. In class III there are a total of 70 children. If there are 5 sections in Class III, how many children are there in each section?
3. 68 birds live in 4 cages in a zoo. How many birds are in each cage?
4. Jack the clown has 99 balloons that he has to share between 9 children at the fair. How many balloons does each child get?
5. Nancy has 96 candies. It has 8 pockets. She wants to put the same amount of candy in each bag. How many will she put in each pocket?
6. Mike organized 24 chairs in 4 rows for a party. How many chairs are there in each row?
7. You have 60 gum balls that you must divide equally into five containers. How many gum balls are in each container?
8. There are 96 books on the shelf. If the books are to be evenly distributed over 4 groups of tables in the class, how many books will there be on each table?
3rd grade math class
From the long division to the HOMEPAGE
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