# Homework Help: Fraction problem

1. Feb 19, 2010

### 1/2"

Hi there!
1)It's a very common problem for me .
I don't get when do I have to multiply or divide a fraction in unitary method e.g.
10 men do 1 work in 40 days
10 men does 3/4 work in 40*3/4 days
or should i do 10 men does 3/4 work in 40*4/3 days
I do't undestand!Plz give me a reason why should I multiply or divide it.
I would be very grateful if anybody does so!
2)The problem:
Forty men finish a piece of work in 40 days; if % men leave the work every ten days,in what time will the whole work be completed.
My try:
I tried to put it like this
40 men in 40 days does 1 work
40 men in 1 day does 1/40 work
40 men in 10 day does 1/40 *10work=1/4
But if I do so I becomes a very very long method.
Isn't there any shorter way.
Thank you.

2. Feb 19, 2010

### BishopUser

you are given 10 men do 1 work in 40 days. Now turn it into more mathematical language: 10 men equal 1 work per 40 days. from this point you should think of it in equation form:

10 men = 1 work / 40 days

to get 3/4 work you have to multiply 1 work * 3/4. What you do to the top of the fraction you must do to the bottom, so 40 days * 3/4 = 30. the final equation is:

10 men = .75 work / 30 days

The key is to realize you want the # of men to say the same, so you don't mess with that side of the equation. just multiply the top and bottom of the fraction by the same value.

3. Feb 20, 2010

### 1/2"

I can understand the later part alright
bUt could you please be more simple here:uhh:
Thanks a lot BishopUser

4. Feb 20, 2010

### Char. Limit

Well, what he starts with is "ten men do one unit of work in forty days".

So, because math is easier, (and I'll take a different approach), I'll change ten men to 10 M, one unit of work to 1 W, and forty days to 40 d. Nothing different, just using different notation.

Of course, here you can see that if 10 men do a unit of work in forty days, they have a rate of one unit of work per forty days. This is written in an equation as:

10 men = 1 unit work / 40 days

or

10 M = 1 W / 40 d