Division
- Meaning of Division
- Division as Repeated Subtraction
- Relation between Multiplication and Division
- Terms of Division
- Properties of Division
- Long Division
- Division without regrouping
Meaning of Division
Division means sharing equally or making equal groups.
Hannah has 4 apples. She shares them equally with Ryan. She gives 1 apple to Ryan and keeps 1 for herself. She has 2 apples left.
She then gives 1 more apple to Ryan and keeps 1 for herself.
Now she has no more apples to share. Each of them has 2 apples.
(Total number of apples) ÷ (Number of people) = Number of apples each person gets.
4 ÷ 2 = 2 is a division fact
It is read as 4 divided by 2 is equal to 2.
Division as Repeated Subtraction
Division is the short way of subtracting the same number again and again.
Help Hannah to divide 9 apples among herself, Irene and Ryan.
Hannah takes away 3 apples and gives 1 to Irene and 1 to Ryan
9 - 3 = 6, She has 6 apples left.
She again takes 3 apples and gives 1 to Irene and 1 to Ryan.
6 - 3 = 3, Now she has 3 apples left. She then gives the remaining 3 to each if them.
3 - 3 = 0, Now she has no apple left to share.
So, 9 ÷ 3 = 3.
Relation between Multiplication and Division
| In multiplication, equal groups are added to get the total number | In division, the total number is divided to get the number in each group. |
| Multiplication Fact: 5 x 2 = 10 2 x 5 = 10 | Division Fact: 10 ÷ 2 = 5 10 ÷ 5 = 2 |
| When the same number is multiplied, the multiplication fact has only one division fact | |
| 5 x 5 = 25 | 25 ÷ 5 = 5 |
Terms of Division
We know, 3 x 2 = 6, so we can say, 6 ÷ 2 = 3, Here 6 is the number to be divided. 2 is the number by which we will do the division and 3 is the result.
| The number to be divided | Dividend |
| The number by which we will do the division | Divisor |
| Result of Division | Quotient |
| Dividend ÷ Divisor = Quotient | |
| Dividend = Divisor x Quotient | |
Here are some examples for you.
| Dividend | Divisor | Quotient | |
|---|---|---|---|
| 8 ÷ 2 = 4 | 8 | 2 | 4 |
| 12 ÷ 4 = 3 | 12 | 4 | 3 |
| 24 ÷ 4 = 6 | 24 | 4 | 6 |
| 27 ÷ 9 = 3 | 27 | 9 | 3 |
| 35 ÷ 5 = 7 | 35 | 5 | 7 |
Properties of Division
| Property | Example |
|---|---|
| Division by the same number: When a number is divided by itself, the quotient is always 1. | 12 ÷ 12 = 1 |
| Division by 1: When a number is divided by 1, the quotient is the number itself. | 12 ÷ 1 = 12 |
| Division of 0: When 0 is divided by any number, the quotient is always 0. | 0 ÷ 12 = 0 |
| Division by 0: Dividing a number by 0 is not possible. | 12 ÷ 0 is not possible. |
Long Division
Let's divide 20 by 5 using long division.
Step 1: Write the numbers like below.
5 20
Step 2: Say the table of 5 till you reach 20. 4 fives are 20.
We write 4 at the quotient's place and 20 below the dividend and subtract. 20 - 20 = 0
4
5 20
20
0
20 ÷ 5 = 4
5 20
Step 2: Say the table of 5 till you reach 20. 4 fives are 20.
We write 4 at the quotient's place and 20 below the dividend and subtract. 20 - 20 = 0
4
5 20
20
0
20 ÷ 5 = 4
Let's divide 15 by 4 using long division.
Step 1: Write the numbers like below.
4 15
Step 2: Say the table of 4 till you reach 15. 3 fours are 12 and 4 fours are 16.
We write 3 at the quotient's place and 12 below the dividend and subtract. 15 - 12 = 3
3
4 15
12
3
We were not able to divide 15 by 4 completely, we got 3 as REMAINDER
15 ÷ 4 = 3, remainder = 3
4 15
Step 2: Say the table of 4 till you reach 15. 3 fours are 12 and 4 fours are 16.
We write 3 at the quotient's place and 12 below the dividend and subtract. 15 - 12 = 3
3
4 15
12
3
We were not able to divide 15 by 4 completely, we got 3 as REMAINDER
15 ÷ 4 = 3, remainder = 3
Division without regrouping
Let's divide 48 by 3 using long division.
Step 1: Arrange the numbers in long division form.
3 48
Step 2: If the left-most digit in the dividend is greater than or equal to the divisor, divide that particular digit. Here 4 is greater than 3. We know 3 ones are 3 and 3 twos are 6. So we write 1 in the quotient's place and the product 3 below the digit and subtract. 4 - 3 = 1
1
3 48
3
1
Step 3: Bring down the next digit (8) to the right of the current remainder. We will get 18. Divide 18 by 3. We know, 6 threes are 18. We write 6 at the quotient's place and 18 below and subtract. 18 - 18 = 0
16
3 48
3
18
18
0
3 48
Step 2: If the left-most digit in the dividend is greater than or equal to the divisor, divide that particular digit. Here 4 is greater than 3. We know 3 ones are 3 and 3 twos are 6. So we write 1 in the quotient's place and the product 3 below the digit and subtract. 4 - 3 = 1
1
3 48
3
1
Step 3: Bring down the next digit (8) to the right of the current remainder. We will get 18. Divide 18 by 3. We know, 6 threes are 18. We write 6 at the quotient's place and 18 below and subtract. 18 - 18 = 0
16
3 48
3
18
18
0
Always remember, after division, the remainder is always smaller than the divisor.