Quotient – Definition with Examples

Definition of Quotient

The number we obtain when we divide one number by another is the quotient. 

For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor. 

Note that, the quotient and the divisor are always smaller than their dividend.

Different Forms of Quotient

The quotient can be an integer or a decimal number.

• When a number is completely divisible by another number, the quotient is a whole number.

For example, 15 ÷ 3 = 5 (whole number)

• When a number is not completely divisible by another number, the quotient is a decimal number.

For example, 15 ÷ 2 = 7.5 (decimal number)

Such divisions leave a remainder, so there is another way of writing answers to such division problems, which is:

15 ÷ 2 = 7 R 1 (where, quotient = 7 and remainder = 1)

Finding Quotients by Repeated Subtraction

It can be helpful to think of division as a repeated subtraction problem. To divide by the repeated subtraction, we subtract the divisor from the dividend till we get a 0 or subtraction is not possible. In this process, the number of times we subtract is the quotient. 

Let’s find the quotient of 20 ÷ 5 using repeated subtraction. 

20 – 5 = 15

15 – 5 = 10

10 – 5 = 5

5 – 5 = 0  (STOP)

We subtracted 5 four times to get a 0, so, 4 is the quotient. That is, 20 ÷ 5 = 4

Finding Quotients by Long Division Method

In math, long division is a method used for dividing large numbers into groups or parts. To divide a number using this method, a division house is drawn. The divisor is written outside the division house, while the dividend is placed within. The quotient is written on top of it.

Long Division involves 5 steps:

D → Divide

M → Multiply

S → Subtract

B → Bring Down

R → Repeat/ Remainder

For example:

Solved Examples

Example 1: Find the quotient: 28 ÷ 3 using repeated subtraction.

Solution:

28 – 3 = 25

25 – 3 = 22

22 – 3 = 19

19 – 3 = 16

16 – 3 = 13

13 – 3 = 10

1- – 3 = 7

7 – 3 = 4

4 – 3 = 1  (3 cannot be subtracted from 1, so we stop here)

We subtracted 3 nine times to get , so, 4 is the quotient. That is, 20 ÷ 5 = 4

Example 2: Find the quotient: 153 ÷ 7 using the long division method.

Quotient = 21; Remainder = 6

Example 3: Jack needs 2 mangoes to make a glass of mango juice. If he has 28 mangoes, how many glasses of mango juice can he make?

Solution: 

Number of mangoes with Jack = 28

Number of mangoes required for 1 glass of juice =  2

Number of glasses of juice Jack can make = 28 ÷ 2

Number of glasses of juice Jack can make = 14 glasses

Practice Problems

Frequently Asked Questions