What is Quotient? Definition, Example, Facts (2025)

  • 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

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Divide 3-digit by 1-digit Numbers

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Divide 4-digit by 1-digit Numbers

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Divide 3-digit by 1-digit Numbers

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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

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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 (2025)

FAQs

What is the meaning of quotient and example? ›

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 the quotient in my own words? ›

Quotient is the answer obtained when we divide one number by another. For example, if we divide the number 6 by 3, we get the result as 2, which is the quotient.

Can you give me an example of a quotient? ›

A quotient is the result of division. The number above the line (the dividend) is divided by the number below the line (the divisor), and the answer is the quotient. For example, in the problem 12 ÷ 3 = 4, 12 is the dividend, 3 is the divisor, and 4 is the quotient.

What describes a quotient? ›

The quotient in math is the number we get when we divide one number by another. In perfect division, a quotient is a whole number with no remainder. But sometimes, a number can't be perfectly divided, and there is a leftover number. This number is the remainder, and can often be expressed as a decimal number.

What is a good sentence for quotient? ›

Many adolescents of that class have very high intelligence quotients. He then assigns these quotients to the regions. They are not in a position to control their muscles, or to respond to the tests made to ascertain their intelligence quotients.

What is a difference quotient example? ›

Example 1: Find the difference quotient of the function f(x) = 3x - 5. Answer: The difference quotient of f(x) is 3. Example 2 : Find the derivative of f(x) = 2x2 - 3 by applying the limit as h → 0 to the difference quotient formula. By applying the limit as h → 0, we get the derivative f ' (x).

What is the quotient in life? ›

Quotient means, the 'degree or amount of a specified quality or characteristic. 2.0 Physical Quotient (PQ) 2.1 Physical quotient, also known as physical intelligence, is an important aspect of personal effectiveness, but most people don't really understand what it is or how they can manage it.

What is the quotient rule example? ›

Let us have a look at the following example given below to understand the quotient rule better. Example: Find f'(x) for the following function f(x) using the quotient rule: f(x) = x2/(x+1). Answer: The derivative of x2/(x + 1) is (x2 + 2x​​​​)/(x + 1)2.

What is another way to say quotient? ›

What is another word for quotient?
fractionpart
divisionproportion
percentageallotment
bitquota
cutsection
162 more rows

What is a quotient person? ›

The quotient refers to a person's ability to tap into their spiritual side, with some people being naturally more spiritually connected than others. Unfortunately, while humans are spiritual beings, not everyone prioritizes doing things that help them achieve spiritual wellness, such as meditation.

What is the quotient of 108 and 12? ›

Answer and Explanation:

108 divided by 12 is equal to 9.

What is another word for quotient? ›

Synonyms: outcome , remainder , computation, result , measure , amount , degree.

What is the estimating quotient of 825 divided by 24? ›

Expert-Verified Answer

825 round off 10 = 830. 24 round off 10 = 20. Now dividing . Hence the estimating quotient is 41.5.

What is the quotient of 18/1000? ›

For example, 18 ÷ 1000 = 18.0/1000 = 0.018. Here, we shifted the decimal point of the dividend to the left by 3 places. Thus, the quotient of 18/1000 is 0.018.

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