# Partial Quotient Algorithm: An Alternative Method for Long Division

My youngest son is a whiz at math – as long as he can figure out problems in his head. But his uncanny ability to make sense of numbers is lost when he looks at a formulaic math problem. When he was learning long division he could frequently calculate the answer in his head, but given a written problem he’d melt into an uncomprehending heap of frustration.

While I don’t remember actually learning the process of long division, I’ve been doing it so long that it’s second nature to me. Nothing I did or said could help my son make sense of the process of long division though, so I began asking around. Miranda at Nurtured by Love came to my rescue when she suggested that I introduce my son to a method called partial quotient algorithm. While it may sound daunting, partial quotient algorithm (or partial quotient division) is a method for dividing numbers that’s much more accessible than the familiar but more abstract long division. It took me a few tries to make sense of this new method (old dog, new tricks and all) but my son was able to grasp it with very little trouble. Bingo! It just took coming at it from a different angle to make the written numbers make sense to him.

Curious? Take a look:

## 7 thoughts on “Partial Quotient Algorithm: An Alternative Method for Long Division”

1. My husband says this is the way he does long division in his head!

2. Thanks so much for this! This is the method my son is learning in school, and I’ve been baffled by it. This explanation is beautifully clear.

1. Kate, I’m so glad to hear that some schools are adopting this method. It truly makes SO much more sense and I think it will be easier for many kids to grasp.

3. Oh, I LOVE this!

4. Thank you! I am going to share this with the math support teacher and see if this will help her students ðŸ™‚

I will also teach this to my advanced students because I think they will like it. We like to play with numbers and this will be fun ðŸ˜‰

5. Great post and great video explaining it! I have a fourth grader who will love this…

Judy

6. Chris says:

Nice videos, I would just like to propose one suggestion. Instead of jumping back down to 20 in the first case, you should split the gap (as close as you can, I would still round to the tens or hundreds depending). Example: You first tried 10, then 100. Your next check should be 50. This method helps you bound in your answer faster then simply stepping up one at a time. Especially in your example in the video. Just a suggestion.