Division of Whole Numbers

Division of whole numbers is discussed here step by step.

1. Division is repeated subtraction.

(a) 25 ÷ 5 = 5

(Repeated Subtraction)

(i) 25 - 5 = 20

(ii) 20 - 5 = 15

(iii) 15 - 5 =10

(iv) 10 - 5 = 5

(v) 5 - 5 = 0

(b) 10 ÷ 2 = 5

(Repeated Subtraction)

(i) 10 - 2 = 8

(ii) 8 - 2 = 6

(iii) 6 - 2 = 4

(iv) 4 - 2 = 2

(v) 2 - 2 = 0

(c) 50 ÷ 10 = 5

(Repeated Subtraction)

(i) 50 - 10 = 40.

(ii) 40 - 10 = 30

(iii) 30 - 10 = 20

(iv) 20 - 10 = 10

(v) 10 - 10 = 0

2. Division is the inverse of multiplication.

(a) (i) 12 × 10 = 120

(ii) 120 ÷ 10= 12

(iii) 120 ÷ 12 = 10

(b) (i) 25 × 5 = 125

(ii) 125 ÷ 5 = 25

(iii) 125 ÷ 25 = 5

3. Relation between Dividend, Divisor, Quotient and Remainder is.

Dividend = Divisor × Quotient + Remainder

To understand the relation between dividend, divisor, quotient and remainder let us follow the following examples:

(a) Divide 537809 by 35 and find the quotient and remainder.

We need to divide the dividend i.e. 537809 by the divisor i.e. 35 to get the quotient and remainder.

5 cannot be divided by 35 as 5 < 35. So, we will move to the next digit of the dividend i.e. 3 and now we have 53 which can be divided by 35 as 53 > 35. We first divide 53 by 35. 35 into 53 is 1 leaving 18.

Then we bring down the next digit of the dividend i.e. 7 and we have 187. Now we divide 187 by 35 so, 35 into 187 is 5 leaving 12.

Again we bring down the next digit of the dividend i.e. 8 and we have 128. Now we divide 128 by 35 so, 35 into 128 is 3 leaving 23.

Similarly, again we bring down the next digit of the dividend i.e. 0 and we have 230. Now we divide 230 by 35 so, 35 into 230 is 6 leaving 20.

And at last we bring down the last digit of the dividend i.e. 9 and we have 209. So, we divide 209 by 35 then, 35 into 209 is 5 leaving 34.

Check the answer of the division:

Dividend = Divisor × Quotient + Remainder

537809 = 35 × 15365 + 34

537809 = 537775 + 34

537809 = 537809

(b) Divide 86228364 by 2768 and check the answer.

We need to divide the dividend i.e. 86228364 by the divisor i.e. 2768 to get the quotient and remainder.

8 cannot be divided by 2768 as 8 < 2768. So, we will move to the second digit of the dividend i.e. 6 and now we have 86 which cannot be divided by 2768 as 86 < 2768. So, we will move to the third digit of the dividend i.e. 2 and now we have 862 which also cannot be divided by 2768 as 862 < 2768. So, we will move to the fourth digit of the dividend i.e. 2 and now we have 8622 which can be divided by 2768 as 8622 > 2768. We first divide 8622 by 2768. 2768 into 8622 is 3 leaving 318.

Then we bring down the fifth digit of the dividend i.e. 8 and we have 3188. Now we divide 3188 by 2768 so, 2768 into 3188 is 1 leaving 420.

Again we bring down the sixth digit of the dividend i.e. 3 and we have 4203. Now we divide 4203 by 2768 so, 2768 into 4203 is 1 leaving 1435.

Similarly, again we bring down the seventh digit of the dividend i.e. 6 and we have 14356. Now we divide 14356 by 2768 so, 2768 into 14356 is 5 leaving 516.

And at last we bring down the last digit of the dividend i.e. 4 and we have 5164. So, we divide 5164 by 2768 then, 2768 into 5164 is 1 leaving 2396.

Now to check the answer of the division:

Dividend = Divisor × Quotient + Remainder

86228364 = 2768 × 31151 + 2396

86228364 = 86225968 + 2396

86228364 = 86228364