 Division | Operations on Numbers | Learning Concepts Operations on Numbers

Division

Division is one of the primary operations. It is the process of sharing a collection of items into equal parts.

• It is inverse operation of multiplication.
• The symbol which is used to denote division is “`÷`”.
• The number that is being divided in the division process is called a dividend.
• The number by which dividend is being divided is called the divisor. A quotient is the result obtained in the division process.
• The remainder is the portion of the dividend that is left over after division. Division

In arithmetic, the division of two numbers represents repeated subtraction. Let’s discuss it with an example.

Examples:

Division of 12 by 4 = 12 `÷` 4

1. 12 – 4 = 8
2. 8 – 4 = 4
3. 4 – 4 = 0

We get 0 in total 3 steps, that is, we need to subtract 4 trice from 12 to get 0.

So, 12 `÷`4 = 3

Division on number line

We can divide numbers using number line.

Examples:

15 `÷` 3

To divide 15 by 3, we need to start from 15 and take jumps of length 3 until we land at 0. To land at 0, we need to take 5 jumps.

Hence, 15 `÷` 3 = 5

Division of 2-digit numbers by a single digit number

Step 1: Choose the digit at the tens place of quotient such that the product of the digit with the divisor is equal to or less than the tens place digit of the dividend. Subtract the product from the tens place number.

Step 2:Continue this process for the ones place also.

Examples:

Find the quotient

a) 42 `÷` 2 b) 56 `÷` 4

a) 42 `÷` 2

Step 1: Step 2: So, divisor = 2, dividend = 42, quotient = 21 and remainder = 0

Hence, 42 `÷` 2 = 21

a)56 `÷` 4

Step 1: Step 2: So, divisor = 4, dividend = 56, quotient = 14 and remainder = 0

Hence, 56 `÷` 4 = 14

Division of 3-digit numbers by a single digit number

Step 1: Choose the digit at the hundreds place of quotient such that the product of the digit with the divisor is equal to or less than the hundreds place digit of the dividend. Subtract the product from the hundreds place number.

Step 2:Continue this process for the tens place and ones place also.

Examples:

a) 366 `÷` 6 b) 425 `÷` 5

a)366 `÷` 6

Step 1: Step 2: So, divisor = 6, dividend = 366, quotient = 61 and remainder = 0 Hence, 366 `÷` 6 = 61

b) 425 `÷` 5

Step 1: Step 2: So, divisor = 5, dividend = 425, quotient = 105 and remainder = 0

Hence, 425 `÷` 4 = 105

Word Problems

Examples:

1. Sanchi has 436 rubber bands. She divided all her rubber bands equally among her 4 cousins. How many rubber bands each one will get?
2. Koyel has 86 centimetres of lengthy ribbon. She divided it into two halves, and gave one half to her friend. What length of the ribbon does she have in her hand now?

1) Sanchi has 436 rubber bands.

If she divided the rubber bands equally among her cousins, then each one of them will get

436 `÷` 4 = 109

Hence, each one of them will get 109 rubber bands.

2) Koyel has 86 centimetres of ribbon

If she divides the ribbon into halves, then each half will have

86 `÷` 2 = 43

Hence, Koyel has 43 cm ribbon in her hand now.  • -