How to Do Division Using Partial Quotients
The method of Partial Quotients is a way to find the answer to a division problem by repeatedly subtracting the same number from the dividend.
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
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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×=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
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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 10×3=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 9×3=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
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