Solving Fraction Problems: Unitary Method

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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.
Please help!
Thank you.

 

[BishopUser]

ok your first example:

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.

 

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I can understand the later part alright
bUt could you please be more simple here

ok your first example:

. 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

.

Thanks a lot BishopUser

 

[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