How to Do Division Using Partial Quotients

A Step-by-step Guide to Doing Division Using Partial Quotients

Certainly, here’s a step-by-step guide to using the Partial Quotients method in the division for grade 4. Let’s use an example: 657 divided by 3.

Step 1: Write the problem out

Start by writing the problem like you would in long division. The number being divided (657) is inside the division bracket, and the number you are dividing by (3) is outside.

3 | 657

Step 2: Make an initial estimate

Estimate a multiple of 3 that can go into 657. It’s okay if it’s not exact. Since we are working with a 4th grader, let’s start with an easy multiple – 100 (because \(100\times = 300\), and 300 is less than 657).

Step 3: Subtract and write the partial quotient

Multiply your estimate by the divisor (3), subtract that from 657, and write the result below. Also, write the estimate above the division bracket. This estimate is your partial quotient.

   100
     _______
3  | 657
   - 300
   -----
     357

Step 4: Repeat the process

Now, repeat the process with the new number (357). Let’s estimate 100 again. Subtract \(300 (100\times3) from 357.

     100 100
     _______
3  | 657
   - 300
   -----
     357
   - 300
   -----
      57

Step 5: Continue until the remainder is less than the divisor

Now, we have 57 left. We can’t subtract 300 anymore, so let’s choose a smaller estimate. Let’s choose 10 (because \(10\times3 = 30\), and 30 is less than 57). Subtract 30 from 57.

          100 100 10
     _______
3  | 657
   - 300
   -----
     357
   - 300
   -----
      57
   - 30
   -----
      27

We can estimate 10 again and subtract 30 from 27.

     100 100 10 10
     _______
3  | 657
   - 300
   -----
     357
   - 300
   -----
      57
   - 30
   -----
      27
   - 30
   -----
      -3

Oops! We’ve gone too far. We can’t subtract 30 from 27. So, let’s remove the last estimate of 10. That leaves us with 27.

     100 100 10
     _______
3  | 657
   - 300
   -----
     357
   - 300
   -----
      57
   - 30
   -----
      27

We can still subtract a multiple of 3 from 27. Let’s choose 9 (because \(9\times3 = 27\), and 27 is less than 27). Subtract 27 from 27.

     100 100 10 9
     _______
3  | 657
   - 300
   -----
     357
   - 300
   -----
      57
   - 30
   -----
      27
   - 27
   -----
       0

Step 6: Add the partial quotients

Now add up all the partial quotients (100, 100, 10, 9) and write that number