Partial Quotient

Partial Quotient Method

Long division is often regarded as one of the most difficult topics to teach. Fortunately, there are strategies that can be taught to make multi-digit division easier to understand and perform.

One of these methods is the Partial Quotients approach. It's a system focused on mental math that will help you understand numbers better. Students solve the equation by subtracting multiples until they approach zero, or as near as possible to zero.


Partial Quotient Definition

A partial quotient is a technique for solving large division problems in mathematics. By allowing the student to see the problem in a less abstract way, the approach employs basic logic.

You may want to start with the Box Method/Area Model if you want to try this technique in your classroom. The Box Method is similar to Partial Quotients in approach, but it is structured differently and works well as an introduction.


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.


Partial Quotient Strategy For Division

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. Divide using partial quotients and 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.


Using Partial Quotients to Divide By 1-Digit Numbers

Partial Division Method

To divide large numbers, partial quotients can be used. This approach divides the problem into smaller bits to make division simpler. The total is then calculated by putting all of the bits back together.

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!


Dividing Decimals With Partial Quotients

Here’s how you can divide Decimals with Remainders using Partial Quotient.

Solve each problem. Round your answer to the nearest tenth -


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Using Partial Quotients to Divide By 2-Digit Numbers

You can also divide larger numbers with partial quotients.

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!


Other Example - 

Example - 

Use partial quotients to divide 596 by 5

Solution - 

Given dividend and divisor values are 596, 5

Now, let's take a step-by-step approach to solve division problems using the partial quotient division method.

Step 1 - Subtract the divisor's greater multiples first. Consider using partial quotients, i.e., repeated subtraction, in which case we must subtract 5 from the dividend 100 times. Then look at what the divide with partial quotients is good for.


Step 2 - Subtract the divisor's lesser multiples.


Step 3 - Finally, add the partial quotients, and you'll have the answer to the division of 596 by 5 using the partial quotient/repeated subtraction method.

FAQs (Frequently Asked Questions)

1. What is Division Using Partial Quotient?

Ans: 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.

2. 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?

Ans: 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.