Partial Quotient

Dhristi JEE 2022-24

Definition of a Quotient

Division results in a different number as a result of dividing a number by another number. Dividends are numbers or integers that get divided, and the integer that divides a given number is the divisor. The remainder of a divisor is that number that does not divide the number entirely. Division symbols are represented by a ÷  or a /. Therefore, we can represent the division method as follows;

Dividend = Quotient × Divisor + Remainder

If the remainder is zero, then; Dividend = Quotient × Divisor

Therefore, Quotient = Dividend ÷ Divisor


Definition of a Partial Quotient

An approach to solving large division problems by using partial quotients is called a partial fraction. By taking a more logical approach to the problem, the student is able to see it less abstractly.


If you want to try this technique in your classroom, you might want to start with the Box Model/Area Model. Partial Quotients and the Box Method are similar in approach, but the Box Method is structured differently and is a good introduction to the quantitative method.


Using Partial Quotients as a Division Strategy

In the division of repeated subtraction and partial quotients, there is a strong correlation. This correlation makes dividing long divisions easy to comprehend and apply. You can easily divide partial quotients according to the three simple steps outlined here. The final quotient can be calculated by adding up each multiplier in the repeated subtraction division method. Long division of numbers can be easily performed by dividing using partial quotients. A fraction of a second after the partial quotient division of the numbers has been performed, the quotient and remainder will be displayed.


How to Divide Using the Partial Quotients Method?

To solve basic division problems, the partial quotients approach (also known as chunking) employs repetitive subtraction. When dividing a big number by a small number.

  • Step 1- Find out an easy multiple of the divisor and deduct from the dividend (for example 100 ×, 10 ×, 5 × 2 ×, etc.) 

  • Step 2 - Continue subtracting until the large number is reduced to zero or the remainder equals the divisor.

  • Step 3 - To find the division answer, add up the multipliers of the divisor that were used in the repeated subtraction.

The partial quotient approach is shown in the diagram below. More explanations and solutions can be found further down the list


Using Partial Quotients to Divide One-Digit Numbers


Method of Partial Division

The use of partial quotients is useful for dividing large numbers. Using partial quotients you can divide the problem into smaller pieces and simplify division. All of the bits are then added back together to get the total.


 Let's try it with 654 ÷ 3.


Step 1 - Start by subtracting multiples of 3 until you reach 0.

A multiple of 3 that goes into 654 is 600, because 3×200=600. Subtract 600 from 654.

You have 54 left. Now subtract another multiple of 3. You can use 30, since 3×10=30.

You have 24 left. Keep going! Subtract 24, since 3×8=24.

You've reached 0, so move to step 2.


Step 2 - Now, see how many times of ‘3’ it took to reach 654.

You broke 654 into 600, 30, and 24. Add the number of times it took 3 to reach each of those numbers.

200 + 10 + 8 = 218

So, 654 ÷ 3 = 218!


Divide Decimals with Partial Quotients 

Using Partial Quotient, You can divide Decimals with Remainders. This will help you find the problem. Make your answer as precise as possible.


Partial Quotients for Dividing by 2-Digit Numbers

Using partial quotients is also an option for dividing large numbers.

Let's try it with 5,520 ÷ 23.


Step 1 - Start by subtracting multiples of 23 until you reach 0.

A multiple of 23 that goes into 5,520 is 4,600, because 23 × 200 = 4,600. Subtract 4,600 from 5,520.

You have 920 left. Now subtract another multiple of 23. You can use 690, since 23 × 30 = 690.

You have 230 left. Subtract 230, since 23 × 10 = 230.

You've reached 0, so move to step 2.


Step 2 - Now, see how many times 23 went into 5,520.

You broke 5,520 into 4,600, 690, and 230. Add the number of times it took 23  to reach each of these -

200 + 30 + 10 = 240

So, 5,520 ÷ 23 = 240! 

FAQs on Partial Quotient

1. How do you Explain Partial Quotients?

Calculations involving large division are often solved using partial quotients. Through this method, students are able to see the problem in a less abstract way, thus laying the foundation for simple logic.

2. What are the Four Strategies for Basic Division?

The purpose of this resource is to teach students four strategies for basic division facts: making equal groups, reverse skip counting, making arrays, and relating to multiplication. As students learn to evaluate the effectiveness of each strategy, they will work through the strategies one by one. 

3. What is also known as the Quotient Method?

Adding and subtracting multi-digit numbers is a simple division procedure in Arithmetic. It makes it possible to divide multi-digit numbers by hand. Divide the dividend by the divisor to obtain the quotient, which is the result of all division problems. 

4. Does the Quotient Involve Multiplication?

The result of a division process is the quotient, and the result of a multiplication process is the product. Dividends and divisors are smaller than the quotient. So, we have a larger product than the two numbers given. 

5. Is the Quotient always Smaller than the Divisor?

Dividends refer to the large group. There are two ways to describe the number of smaller equal groups. “Divisor” is the number of smaller equal groups and “quotient” is the number of objects in each smaller group. There is always a remainder that is less than the divisor.


For further information on the topic download Vedantu’s app or refer to the website for free.

6. What is Division Using Partial Quotient?

The division of partial quotients is similar to the division of repeated subtraction. A partial quotient refers to a method for solving large division problems in mathematics. An alternative to the traditional long division method is the partial quotient method. This partial quotient division method is used to make multi-digit division simple and easy to understand and perform.


To solve simple division problems, the partial quotients method employs repeated subtraction logic. By following the three simple steps outlined here, you can make manual math division calculations a breeze. As a result, use partial division and get the result quickly.

  • Subtract an easy multiple of the divisor (such as 100x, 300x, 40x, etc., which are all multiples of 10) from the dividend.

  • Subtract the large number until the remainder is less than the divisor or the large number is reduced to zero.

  • To find the division answer, add up the partial quotient multipliers that were used in the repeated subtraction.

7. How Do You Do Partial Quotient Division? How Do You Calculate the Final Quotient in a Partial Quotient Method? How to Divide Numbers Using the Partial Quotient Method Easily?

The division of partial quotients and the division of repeated subtraction are closely related. It is simple to comprehend and apply when dividing long divisions. Follow the three simple steps outlined here to easily perform partial quotient division. In the repeated subtraction division method, you can calculate the final quotient result by adding up all the used multipliers. With the help of our Division Using Partial Quotient Calculator, you can easily perform a long division of numbers. Within a fraction of a second, it will display the quotient and remainder for the division of numbers using the partial quotient division method.

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