long division question

[rivers]

I was doing the problem 7984/66, and I came across some difficulty. I got 12 after the first time, and realized it couldn't be right. Did it on a calculator and got 120. After reviewing the problem, it seems I have to ask myself, how many times does 66 go into 64? Then, place a 0 next to the 12. Typically (for the problems I've done), if the divisor can't go into the number, I would just call it the remainder. Why is this one different*?

*Do all the numbers in the dividend have to factor into the quotient? I noticed, in other problems, the remainder is usually a step after all the numbers from the dividend have been brought down.

 

[Denis]

Hmmm....are you saying you cannot perform a division by hand?
What grade are you in?

7984 divided by 66 = 120 with remainder of 64 ; do you understand that?

 

[rivers]

I understand what the answer is. I'm confused about where the 0 comes from whilst doing it by hand.

 

[Denis]

      120
     ----
 66 / 7984
     66
     --
     138
     132
     ---
       64
        0
       --
       64

OK? Ya'll come back now hear?

 

[rivers]

      12
     ----
 66 / 7984
     66
     --
     138
     132
     ---
       64

This is what it looked like when I did it the first time. I'm still confused, I don't understand where the 0 comes from and why it's carried. I figure the 0 is from 66 going into 64 0 times, but on most other problems, the 64 is usually just called the remainder without having to add a zero, why is this one different?

 

[Denis]

This is what it looked like when I did it the first time. I'm still confused, I don't understand where the 0 comes from and why it's carried. I figure the 0 is from 66 going into 64 0 times, but on most other problems, the 64 is usually just called the remainder without having to add a zero, why is this one different?

The 0 comes from 66 goes in 64 ZERO times. This one is not different...

 

[DrSteve]

This actually brings up something that confuses a lot of students. In general, when dividing a smaller number by a larger number the quotient is 0 and the remainder is the smaller number.

In this example, dividing 64 by 66 gives a quotient of 0 and a remainder of 64.

Here is a physical example. Suppose there are 64 pennies on the floor. You want to put each group of 66 in its own jar, and throw away any that are left over. What happens? Well you will fill 0 jars and throw away 64 pennies.

 

[rivers]

I should clarify, I meant different from a problem like 2396/66. At the end of that problem, there is 20 leftover, 66 goes into 20, zero times. Yet, on that problem, adding a zero would make the answer 360, instead of 36, the former being incorrect.

 

[DrSteve]

I should clarify, I meant different from a problem like 2396/66. At the end of that problem, there is 20 leftover, 66 goes into 20, zero times. Yet, on that problem, adding a zero would make the answer 360, instead of 36, the former being incorrect.

If you actually put in the zero here it would be placed after the decimal point. But 36.0 is the same as 36, so there is no need to write the zero.

It seems that you're not be careful about where you place your digits when doing your long divison.