Dividend, Divisor, Quotient and Remainder

# Dividend, Divisor, Quotient and Remainder

Dividend, Divisor, Quotient and Remainder

Division is the process of sharing things into equal groups.

Suppose we have 15 balls and these are to be shared equally into 3 children.

You can see from the following figure that each group has 5 balls. It means each child will get 5 balls.

Division is denoted by the symbol ‘÷’.

So, the statement when 15 balls are shared equally among 3 children, each child will get 5 balls, can be written in division form as:

15 ÷ 3 = 5

In the above division equation, 15 is called dividend, 3 is divisor and 5 is quotient.

Thus,

The number which is to be divided is called the dividend.

The number which divides the dividend is called the divisor.

The result is called the quotient.

The leftover, if any, is called the remainder. Here, no balls are leftover, therefore the remainder is 0.

Division is a repeated subtraction.

Division can be done using repeated subtraction.

Let us divide 15 by 5. Subtract 5 from 15 again and again until you get zero.

Step 1: Subtract 5 from 15.

15 – 5 = 10

Step 2: Subtract 5 from 10.

10 – 5 = 5

Step 3: Subtract 5 from 5.

5 – 5 = 0

We subtracted 3 times.

Thus, 15 ÷ 5 = 3

Dividend, Divisor, Quotient and Remainder Formula

There is a relationship between the dividend, divisor, quotient and the remainder. This relationship is called the dividend, divisor, quotient and the remainder formula.

Let us divide 122 by 5 and find the quotient and the remainder.

Here, quotient is 24 and remainder is 2. The dividend is 122 and the divisor is 5.

If we multiply quotient (24) by the divisor (5) and add the remainder (2), we get the dividend (122).

The above relation is called the dividend, divisor, quotient and remainder formula.

According to this formula:

Quotient × Divisor + Remainder = Dividend

Or

Dividend = Quotient × Divisor + Remainder

Dividend Definition

As discussed earlier, the number to be divided is called the dividend.

For example: If 12 is divided by 3, 12 is called the dividend.

Divisor Definition

As discussed earlier, the number by which the dividend is divided is called the divisor.

For example: If 12 is divided by 3, 12 is called the dividend and 3 is called the divisor.

You can see the divisor is shown in the above division problem.

Quotient Definition

We know that the result obtained after division is called the quotient.

For example: If 13 is divided by 5, the quotient is 2.

Remainder Definition

The number which is leftover after finding the quotient is called the remainder.

For example: If 13 is divided by 5, the quotient is 2. After division, 3 is left over. Therefore, 3 is the remainder.

You can see the remainder is shown in the above division problem.

Properties of Division

1. If we divide 0 by another number, the quotient is always zero.

For example:

(i) 0 ÷ 8 = 0

(ii) 0 ÷ 16 = 0

(iii) 0 ÷ 245 = 0

(iv) 0 ÷ 136 = 0

(v) 0 ÷ 2748 = 0

2. If a number is divided by 1, the quotient is always the number itself.

For example:

(i) 6 ÷ 1 = 6

(ii) 36 ÷ 1 = 36

(iii) 216 ÷ 1 = 216

(iv) 475 ÷ 1 = 475

(v) 6812 ÷ 1 = 6812

3. If a number is divided by itself, the quotient is always 1.

For example:

(i) 9 ÷ 9 = 1

(ii) 57 ÷ 57 = 1

(iii) 375 ÷ 375 = 1

(iv) 1746 ÷ 1746 = 1

(v) 7583 ÷ 7583 = 1

Let us consider a few examples to verify the answer of division.

Example 1: Divide 67 by 3. Find the quotient and remainder.

Solution: Let us divide 67 by 3.

Here, Dividend = 67

Divisor = 3

Quotient = 22

Remainder = 1

Example 2: Divide 962 by 15. Find the quotient and remainder.

Solution: Let us divide 962 by 15.

Here, Dividend = 962

Divisor = 15

Quotient = 64

Remainder = 2

Example 3: Divide 4368 by 9. Verify the answer.

Solution: Let us divide 4368 by 9.

Here, Dividend = 4368

Divisor = 9

Quotient = 485

Remainder = 3

Now, let us verify the answer.

Quotient × Divisor + Remainder = Dividend

485 × 9 + 3 = 4368, which is dividend.

Hence, verified.

Example 4: Divide 8569 by 6. Verify the answer.

Solution: Let us divide 8569 by 6.

Here, Dividend = 8569

Divisor = 6

Quotient = 1428

Remainder = 1

Now, let us verify the answer.

Quotient × Divisor + Remainder = Dividend

1428 × 6 + 1 = 8569, which is dividend.

Hence, verified.

Related Topics:

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Multiplicand and multiplier

Dividend, divisor, quotient and remainder

Natural numbers

Whole numbers

Properties of rational numbers

Are all integers rational numbers?

Find five rational numbers between 3/5 and 4/5