**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:**

**Dividend, divisor, quotient and remainder**

**Properties of rational numbers**

**Are all integers rational numbers?**

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