Quotient

The quotient is the number obtained by dividing one number by another. For example, if we divide the number 6 by 3, the result so obtained is 2, which is the quotient. It is the answer from the division process. The quotient can be an integer or a decimal number. For exact divisions such as 10 ÷ 5 = 2, we have an integer as a quotient, and for divisions such as 12 ÷ 5 = 2.4, the quotient is a decimal. In the division process with decimal quotient as answer, the decimal part of the quotient is the remainder of the division.

Generally, knowing the quotient helps in understanding the size of the dividend compared to the divisor. The formula for quotient is dividend by the divisor. A quotient can be larger than the divisor but lesser than the dividend. Let us explore and know more about the quotient and the methods to find the quotient.

Table of Contents

What is Quotient in Division?

The division is the process of repetitive subtraction. The number of times of subtraction is equal to the quotient. The division is denoted by a mathematical symbol(÷) which consists of a short horizontal line with a dot each above and below the line. The quotient is the final answer of this division process. Let us explore with an example to understand the quotient in division. The example shows division as a method of grouping objects equally in groups. The box below contains 16 balls. Let us divide them into 4 equal groups. We can see that there are 4 balls placed in each group. The division statement for the picture above can be written as 16/4 = 4.

Example of Quotient

Division as repeated subtraction can be seen here. Let us consider a bowl with 14 fish in a larger bowl, and are being equally distributed into two smaller bowls. As you can be observed, there are 14 fish in the larger bowl. We have to divide them equally into the two smaller bowls. Here the 7 fishes in each own can be taken as the quotient of this division. By taking every fish (subtracting) from the large bowl and placing them in the small bowls alternately, we get 7 fish in each small bowl. The division statement for this example can be written as 14/2 = 7.

Let us take another example in which we divide the bar of chocolate by having 12 pieces into 3 equal parts. By dividing the bar of chocolate, we get 4 pieces in each part. The division statement for this bar of chocolate can be written as 12 ÷ 4 =  3. Here the 3 parts obtained are the quotient.

Finding Quotient using Division

Division is one of the four basic mathematical operations, the other three being Addition, Subtraction, and Multiplication. In simple words, division can be defined as the splitting of a large group into equal smaller groups. The quotient is the result of the division process. On completion of the division process, the quotient is obtained. Division can be introduced by considering objects from our daily life like slices of a pizza or a bar of chocolate. We can see that a pizza can be divided into 4 slices, or a bar of chocolate can be divided and the number of pieces obtained is the quotient.

Imagine you have a chocolate bar with 12 pieces. You want to share it with your friend. Can the bar be divided equally between the two? Will there be any leftover pieces? As you can see here, we have divided this bar of chocolate into 2 parts. Both you and your friend will get 6 pieces of chocolate each. Did you notice? No piece of chocolate remains unshared. Hence, there is no remainder. We can write the division statement for the example above as 12 ÷ 2 = 6. Here each of the numbers in the division can be designated with special terms. Let us check the following terms closely related to the quotient.

Terms Descriptions Values
Dividend The total pieces that are to be shared 12
Divisor The number of equal groups that are to be made 2
Quotient The number of pieces in each group 6
Remainder The remaining piece that is not part of any group 0

This example can also be mathematically represented as below:

Quotient and Other Terms in Long Division

Know about Quotients

Quotient in mathematics can be defined as the result of the division between a number and any divisor. It is the number of times the divisor is contained in the dividend without the remainder being negative. In the image given below, divisor 2 is contained 6 times in the dividend 12. The quotient is larger or smaller than the divisor but is always smaller than the dividend.

Quotient and Related Terms

Division Method to find Quotient

Division method follows the use of divisor and the dividend find the quotient. The quotient can be calculated by dividing dividend with dividend. Quotient = Dividend ÷ Divisor. This is the most common method used to solve problems on division. Let us understand this with the help of examples. Let us solve 435 ÷ 4. The number 435 can be represented on an abacus with its hundredth, tens, and units place respectively.

The following two steps are helpful to understand the division process and to find the quotient.

  • Step 1:Take the first digit of the dividend. If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top. Subtract the result from the digit and write below. Here, the first digit is 4 and it is equal to the divisor. S o, 4 ÷ 4 = 1 is written on top, inside the yellow box below. The result 4 ×4 = 1 is subtracted from the digit and 0 is written below. Next drop the second digit or the digit in the ten’s place beside 0.
  • Step 2: We can see that we have 03 as the result of step 1. Repeat the same step of checking if this number is greater or smaller than the divisor. Since 03 is less than 4, we cannot divide this number. Hence, we write a 0 on the top and drop the digit on the unit place beside 3. Now, we have 35. As 35 > 4, we can divide this number and write 35 ÷ 4 = 8 on top. Subtract the result 4 × 8 = 32 from 35 and write 3. 3 is known as remainder and 108 is called the quotient.
  • Quotient and Remainder in Long Division

Verification of Division Result: We can easily verify if our answer is correct or wrong. As division is the reverse of multiplication, let us find out how we can verify our answer using this information. For example, 6/2 = 3 and remainder is 0. In other words,  6 = 2 × 3 + 0. This can be expressed as: Dividend = Divisor × Quotient + Remainder Let us reconsider the example discussed above, where theLet us reconsider the example. Here the dividend is 435, the divisor is 4, the quotient is 108, and the remainder is 3. Substituting the value in the formula, we get 435 = 4 × 108 + 3. Therefore, our answer is correct.


Important Topics

Given below is the list of topics that are closely connected to quotient. These topics will also give you a glimpse of how such concepts are covered in Cuemath.


FAQs on Quotient

How do you Find Quotient in Division?

The quotient in the division can be found by the formula: Dividend ÷ Divisor = Quotient. Let us understand this by a simple example of 12÷ 4 = 3. Here 12 is the dividend, 4 is the divisor, and 3 is the quotient. 

Is Quotient Always a Whole Number?

The quotient is not always a whole number. The quotient can be a whole number or a decimal number. For perfect division, such as 16 ÷ 2 = 8, a quotient is a whole number and for divisions having remainder the quotient is a decimal number. Division example such as 16 ÷ 5 = 3.2 has a decimal number as a quotient.

What is Quotient in Maths?

The result of the division is known as a quotient in mathematics. In the example, 63/9 = 7,7 will be the quotient since 7 groups can be formed with 9 units in each group. The quotient is larger or smaller than the divisor and is lesser than the dividend.

What is the Difference Between Quotient and Remainder?

The number of remaining units which cannot be part of any smaller group is known as the remainder. The quotient is equal to the number of times the divisor goes in the dividend. For perfect divisions, a quotient is a whole number, and the remainder is zero. In general, a remainder is sometimes accounted in a quotient and the quotient is a decimal number.

How can we Verify the Quotient in Division?

Division is also known as inverse multiplication. We can verify our results by using the following formula: Dividend = (Divisor x Quotient) + Remainder

How do you Find the Quotient through Long Division?

To find quotient through the long division method check the number of times the divisor goes in the dividend. This is the dividend. Subtract the answer of the product of the divisor and the quotient from the dividend. This difference gives the remainder. The entire terms involved in the division process can be presented in the form of an equation as Dividend = Divisor ×Quotient + Remainder. 

What is the Quotient of 14 and 7?

The quotient of the numbers 14 and 7 is 2. The number 14 is the dividend and the number 7 is the divisor and we have 14 ÷ 7 = 2.

What is the Difference Between Quotient and Product?

The quotient is the result of a division process and the product is the result of the multiplication process. The quotient is smaller than the dividend and the divisor. The product is larger than the given two numbers.


Solved Examples

Example 1: Rs. 4000 is distributed among 25 women for the work completed by them at a construction site. Calculate the amount given to each woman.

Solution

The total amount is Rs.4000. The number of women at work is 25. We have to calculate the amount given to each woman. To do so, we have to divide 4000 by 25 using the long division method and find the quotient.

Long Division of 4000 by 25

Each woman will be given Rs.160. Therefore, the amount given to each woman is 160.

Example 2: 66 people are invited to a birthday party. The suppliers have to arrange tables for the invitees. 7 people can sit around a table. How many tables should the suppliers arrange for the invitees?

Solution:

The total number of invitees is 66. The number of people who can sit around one table is 7. We divide 66 by 7 using the long division method and find the quotient.

Long Division of 66 by 7

Since 9 is the quotient, we need 9 tables. With 9 tables, we will still have 3 (which is the remainder) people without a place to sit. Hence, the suppliers should arrange one more table for them. The total number of tables to be arranged by the suppliers = 9 + 1 = 10.  Therefore, the required number of tables is 10.

Example 3: Calculate the number of hours in 2100 minutes.

Solution:

We know that 1 hour is equal to 60 minutes. To find the number of hours in 2100 minutes, we have to divide 2100 by 60 and find the quotient.

Long Division of 2100 by 60

Therefore, there are 35 hours in 2100 minutes.

Example 4: When the teacher of class 6 asked a question, some students raised their hands. But instead of raising one hand, each student raised both their hands. If there are 56 hands in total, how many students raised their hands?

Solution:

The number of hands raised is 56. To find the number of students who raised their hands, we have to divide 56 by 2 and find the quotient, because each student raised both hands.

Long Division of 56 by 2

Therefore, 28 students raised their hands.

Example 5: Emma needs 3 apples to make a big glass of apple juice. If she has 51 apples, how many glasses of juice can she make?

Solution:

The total number of apples with Emma is 51. The number of apples needed for one glass of juice 3. To find the number of glasses of juice, we divide 51 by 3 and find the quotient.

Division of 51 by 3

Emma can make 17 glasses of juice with 51 apples. Therefore, the number of glasses of juice is 17.

Practice Questions on Quotient

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
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