Long division with trial quotient

[Snena]

I can't figure out how they got 82 using trial quotient in this long division problem. I know the answer is 82, but I don't understand the steps to get there. I'll post a picture of the problem first then the guide they gave me.
I get stuck on the first part when divide the 22 by 3 its 7, not an 8 to end up with 82. Hmmm. I'm so confused.

 

[Dr.Peterson]

I can't figure out how they got 82 using trial quotient in this long division problem. I know the answer is 82, but I don't understand the steps to get there. I'll post a picture of the problem first then the guide they gave me.View attachment 28758View attachment 28759
I get stuck on the first part when divide the 22 by 3 its 7, not an 8 to end up with 82. Hmmm. I'm so confused.

Do they not show you how to adjust your "trial quotient"? The reason they call it "trial" is that you are trying it, and then changing it if it doesn't work. The example you show doesn't involve that step, so they must give you another example that does. You may just need to read on in your book.

When you try the quotient 7, you then multiply 28 by 7 and get 196. When you subtract that from 229, you get 33. This remainder is greater than the divisor, 28, and that triggers the adjustment. You need a larger quotient, so you increase it from 7 to 8, and try again.

This is how the process works. The 7 was not an error, just a first try; it reveals itself as such when you use it, and then you change it. And you don't know it's wrong by comparing with a known answer; you know that you need to adjust it by following the process, and so ultimately discover what the right answer is.

 

[Snena]

Thanks! That solves it for me. I'm gonna go check if the book says it in the next few pages.