# Homework Help: Division question

1. Oct 24, 2004

### roger

HI

please can someone help me with this quick question on division :

If I have to do 3 divided by 4
____
4 |3

4 doesn't go into 3 so I put a zero on top .

When it gets to 4 into 2(from 30-4x7), it doesn't go, so why don't I put a zero on top but instead put a zero beside the 2 to make it 20 ?

thankyou

roger

2. Oct 24, 2004

### dav2008

I have no idea what you're doing.

If you're doing 3 divided by 4 using long division:

http://home.comcast.net/~iberiaforums/division.GIF [Broken]

Last edited by a moderator: May 1, 2017
3. Oct 24, 2004

### arildno

roger:
Do you want to perform 3:4 or 4:3?

4. Oct 24, 2004

### roger

DEAR ARILDNO,

I AM TRYING TO DO 3 DIVIDED BY 4 LONG DIVISION

BUT WHY DONT I PUT A ZERO ON TOP FOR 4 INTO 2 ?

ROGER

5. Oct 24, 2004

### dav2008

You never put a 0 on top.

What you do in the first step is put a decimal point on top.

6. Oct 24, 2004

### roger

when you do 7x4 =28

and then 30 minus 28 = 2.

from here

4 doesnt go into 2 so why don't I put a zero on top ?

This is what I want to know ....

thanx

roger

7. Oct 25, 2004

### arildno

Now, since to write down the long-division algoritm is a bit difficult (and besides, we do it differently in Norway from the US), I will show you the RATIONALE behind the long division technique instead; long division is simply a condensed version of what I'll present.

1. What is meant by "division" in this case?
Ordinarily, "division" is meant to be that process that rewrites a number, given as a FRACTION, into the equivalent DECIMAL REPRESENTATION of that number (which, as it happens, is a particular TYPE of fractional representation).
2. Let's look at the number given by fraction 3/4

We want to write 3/4 in its decimal representation, that is to find digits $$a_{i}$$ between 0 and 9, so that we have:
$$\frac{3}{4}=0.a_{1}a_{2}a_{3}....$$
Where the notation $$0.a_{1}a_{2}a_{3}....$$ MEANS:
$$0.a_{1}a_{2}a_{3}....\equiv\frac{a_{1}}{10}+\frac{a_{2}}{100}+\frac{a_{3}}{1000}++$$

3. Let's start!
a) We note that 3<4, so our first step is to multiply 3/4 with an appropriate representation of the number "1":
$$\frac{3}{4}=1*\frac{3}{4}=\frac{10}{10}*\frac{3}{4}=\frac{1}{10}*(\frac{30}{4})$$
Henceforth, we will work with the expression included in the parenthesis.
b)
We note that 30>4, and the greatest multiple of 4 which is less than 30, is 4*7=28.
Hence, we write 30=4*7+2
We therefore have the equality:
$$\frac{30}{4}=\frac{4*7+2}{4}$$
c)We now use the fact that we can split up a sum in the numerator into a sum of fractions:
$$\frac{4*7+2}{4}=\frac{4*7}{4}+\frac{2}{4}=7+\frac{2}{4}$$
The last step follows since 4 is a common factor in both the numerator and denominator in the first fraction.
d) Hence we have shown:
$$\frac{3}{4}=\frac{1}{10}*(7+\frac{2}{4})$$
This can be rewritten as:
$$\frac{3}{4}=\frac{7}{10}+\frac{1}{10}(\frac{2}{4})=0.7+\frac{1}{10}(\frac{2}{4})$$
e) We will now work with the parenthesized 2/4.
Since 2<4, we multiply 2/4 by an appropriate version of 1:
$$\frac{2}{4}=1*\frac{2}{4}=\frac{10}{10}*\frac{2}{4}=\frac{1}{10}*(\frac{20}{4})$$
f) We note that 20=5*4, so we have:
$$\frac{2}{4}=\frac{1}{10}*(\frac{5*4}{4})=\frac{1}{10}*(5)=\frac{5}{10}$$
g) We now look back at the equation in d):
$$\frac{3}{4}=0.7+\frac{1}{10}(\frac{2}{4})$$
With the result from f), we have:
$$\frac{3}{4}=0.7+\frac{1}{10}(\frac{5}{10})=0.7+\frac{5}{100}=0.7+0.05=0.75$$

And that's our result..

Last edited: Oct 25, 2004
8. Oct 25, 2004

### HallsofIvy

I'm confused about your question "WHY DONT I PUT A ZERO ON TOP FOR 4 INTO 2 ?" because I certainly WOULD put a 0 on top!

4 goes into 3 0 times so I would put a 0 before the decimal point and continue:

__0.
4) 3.0

Now, 4 divides into 30 (ignore the decimal point now- we've already taken care of it) 7 times: 4*7= 28

__0.7
4) 3.00
_28_
20
and now 4 divides into 20 5 times, evenly

__0.75_
4) 3.000
_2 8__
20
20

Of course, you don't HAVE to put the "0 on top" because 0, after all, means NOTHING! 0.75 is the same as .75 although I think you will find that "0.75" is preferred in "formal" writing.

9. Oct 25, 2004

### roger

I'm confused about your question "WHY DONT I PUT A ZERO ON TOP FOR 4 INTO 2 ?" because I certainly WOULD put a 0 on top!

4 goes into 3 0 times so I would put a 0 before the decimal point and continue:

__0.
4) 3.0

Now, 4 divides into 30 (ignore the decimal point now- we've already taken care of it) 7 times: 4*7= 28

__0.7
4) 3.00
_28_
20
and now 4 divides into 20 5 times, evenly
this is where my concern was...
I thought it was 4 divides into 2 NOT 20.
So is that to say because the decimal point has been put down, it is really the calculation of 30 divided by 4 ?
Because if it had been 2 instead of 20, my question was if 4 does not go into 2, then why do I not put a zero on top to indicate this .And then I would have brought down a zero to make it 20 and proceed from there......
If I ever have to bring down a zero, where does it come from ?
__0.75_
4) 3.000
_2 8__
20
20

Of course, you don't HAVE to put the "0 on top" because 0, after all, means NOTHING! 0.75 is the same as .75 although I think you will find that "0.75" is preferred in "formal" writing

10. Oct 26, 2004

### HallsofIvy

"Because if it had been 2 instead of 20, my question was if 4 does not go into 2, then why do I not put a zero on top to indicate this "

And my answer was you certainly can "put a zero on top to indicate this."

You don't HAVE to since ".75" is commonly understood as "0.75" although, in my opinion, 0.75 is better.

11. Oct 26, 2004

### roger

It still doesn't answer my query because if I had done it my way, I would have got an answer of 0.705

This is wrong it should be 0.75 but I'm referring to the zero after the 7 not before the decimal point ?

Roger

12. Oct 26, 2004

### faust9

Ok, I don't understand why you WANT to put the zero on the top?

Lets walk through an easy example the way you want to do it and the correct way:

116/4

___2
4)116

2*4=8

11-8=3

Now 3/4=0

___20
4)116

bring down the 6

36/4=9

___209
4)116

Does that look like the correct answer? No. The reason you don't put the 0 on the top is that you don't redivide the remainder from one step to the next.

Good luck.

13. Oct 27, 2004

### dav2008

Your question is like asking "why don't you add a zero when you divide 30/5 and get 6, not 60"

You just don't. That's how it's done.