What is Quotient? Definition, Example, Facts (2024)

  • Definition of Quotient
  • Different Forms of Quotient
  • Finding Quotients by Repeated Subtraction
  • Finding Quotients by Long Division Method
  • Practice Problems
  • Frequently Asked Questions

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.

What is Quotient? Definition, Example, Facts (1)Begin here

Divide 2-digit by 1-digit Numbers

Choose the Correct Missing Part of DIvision Equation Game

Play

Divide Decimals

Complete Division Patterns of Decimal Numbers Game

Play

Divide 3-digit by 1-digit Numbers

Complete the Division Equation by FIlling the Quotient or Divisor Game

Play

Divide 4-digit by 1-digit Numbers

Complete the Division Equation Game

Play

Introduction to Division

Complete the Division Expression for Arrays Game

Play

Introduction to Division

Complete the Division Expression for Equal Groups Game

Play

Division Facts of 2

Complete the Division Patterns Game

Play

Divide 3-digit by 1-digit Numbers

Complete the Division Solution Game

Play

Divide 2-digit by 1-digit Numbers

Complete the Division Solution Where Dividend is Between 6-9 Game

Play

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)

Related Worksheets

ViewViewViewViewViewViewViewViewViewView

Finding Quotients by Repeated Subtraction

It can be helpful to think of division as a repeated subtraction problem. To divide by repeated subtraction, we subtract the divisor from the dividend till we get a 0 or until subtraction is no longer 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 five steps:

D → Divide

M → Multiply

S → Subtract

B → Bring Down

R → Repeat/ Remainder

For example:

What is Quotient? Definition, Example, Facts (22)

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

10 – 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.

What is Quotient? Definition, Example, Facts (23)

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

What is Quotient? Definition, Example, Facts (24)

Number of glasses of juice Jack can make = 14 glasses

Practice Problems

1

Find the quotient: 15 ÷ 3.

3

5

4

2

CorrectIncorrect

Correct answer is: 5
We know that, 3 ✕ 5 = 15, so, 15 ÷ 3 = 5.

2

Find the quotient: 90 ÷ 3.

30

25

20

35

CorrectIncorrect

Correct answer is: 30
We know that, 30 ✕ 3= 90, so, 90 ÷ 3 = 5.

3

Find the quotient 400 ÷ 10.

20

40

60

50

CorrectIncorrect

Correct answer is: 40
We know that, 40 ✕ 10 = 400, so, 400 ÷ 10 = 40.

Frequently Asked Questions

Quotient is the result of dividing two numbers and product is the result of multiplying two numbers.

Dividend → the number to be divided

Divisor → the number by which a dividend is divided

Quotient → the result of dividing the dividend by the divisor

Remainder → the number leftover after division

The leftover part after division is known as the remainder while the quotient is the number we obtain when we divide one number by another. For perfect divisions, a quotient is a whole number, and the remainder is zero. In general, a remainder is sometimes accounted into the quotient, making it a decimal number.

Dividend = Divisor × Quotient + Remainder

What is Quotient? Definition, Example, Facts (2024)
Top Articles
Latest Posts
Article information

Author: Van Hayes

Last Updated:

Views: 5949

Rating: 4.6 / 5 (66 voted)

Reviews: 89% of readers found this page helpful

Author information

Name: Van Hayes

Birthday: 1994-06-07

Address: 2004 Kling Rapid, New Destiny, MT 64658-2367

Phone: +512425013758

Job: National Farming Director

Hobby: Reading, Polo, Genealogy, amateur radio, Scouting, Stand-up comedy, Cryptography

Introduction: My name is Van Hayes, I am a thankful, friendly, smiling, calm, powerful, fine, enthusiastic person who loves writing and wants to share my knowledge and understanding with you.