Fraction problem

[bronx.system]

i got stuck trying to work this problem out hoping someone here can aware me what im doing wrong would be much appreciated.

three men paint half of a house in 1 day. How long will it take 5 men to paint whole house?

what i tried to do

three men paint whole house in 48 hours
1 man paints whole house 48x3 = 144 hours
5 men paint whole house 5/144 = 28.8

but how would you write that as a faction?
28.8 / 24 = 1.2
1 1/5 days

is there another way to work the fraction 28.8/24 ? more easier way i mean

 

[tkhunny]

3 guys 1/2 house 1 day ==> 1 guy 1/6 house 1 day
6 guys 1/1 house 1 day ==> 1 guy 1/6 house 1 day
5 guys 5/6 house 1 day <== 1 guy 1/6 house 1 day
5 guys 6/6 house (6/5)(1 day)

 

[MarkFL]

I would use the proportion 3 guys is to 1/2 house per day as 5 guys is to 1 house per x days:

\(\displaystyle \displaystyle \frac{3}{\frac{\frac{1}{2}}{1}}=\frac{5}{\frac{1}{x}}\)

\(\displaystyle \displaystyle 6=5x\)

\(\displaystyle x=\dfrac{6}{5}\)

 

[bronx.system]

thank you all but this is what i was looking for.

I would use the proportion 3 guys is to 1/2 house per day as 5 guys is to 1 house per x days:

\(\displaystyle \displaystyle \frac{3}{\frac{\frac{1}{2}}{1}}=\frac{5}{\frac{1}{x}}\)

\(\displaystyle \displaystyle 6=5x\)

\(\displaystyle x=\dfrac{6}{5}\)

any chance someone can just briefly explain how to solve this s: i read the section on proportions and ratios from the above post but i dont understand how markfl got \(\displaystyle \displaystyle 6=5x\).
or can someone at least tell me what to read up on?

 

[MarkFL]

When dividing by a fraction, "invert and multiply." For example:

\(\displaystyle \displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}= \frac{a}{b}\cdot\frac{d}{c}=\frac{ad}{bc}\)

 

[bronx.system]

When dividing by a fraction, "invert and multiply." For example:

\(\displaystyle \displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}= \frac{a}{b}\cdot\frac{d}{c}=\frac{ad}{bc}\)

sorry really embarrassing but does this make sense

3x1 = 3
.5 x 5 = 2.5

= 6/5
=1 1/5
not sure what thats called making it a proper fraction from improper?
what about the 3/2.5 to 6/5 is that called making it equivalent fraction?

 

[JeffM]

sorry really embarrassing but does this make sense

3x1 = 3
.5 x 5 = 2.5

= 6/5
=1 1/5
not sure what thats called making it a proper fraction from improper?
what about the 3/2.5 to 6/5 is that called making it equivalent fraction?

I am getting mixed up reading this thread. Your initial post got the correct answer, and you seemed to be asking about presentation of fractions. I have no idea what you are asking above.

3 men paint 1/2 a house in one day.

So the 3 men can paint the house in two days.

Thus it takes 6 man-days to paint the house.

Using 5 men, that means the house can be painted in \(\displaystyle \dfrac{6\ man-days}{5\ men} = \dfrac{6}{5}\ days.\)

A fraction where the absolute value of the numerator is not less than the absolute value of the denominator is called an improper fraction.

There are a number of accepted ways to deal with improper fractions. One is to leave them in so-called improper form. (I like that one because I am lazy.)

Another way, used by electronic calculators, is to reduce them to decimal form, like this:

\(\displaystyle \dfrac{6}{5} = \dfrac{12}{10} = \dfrac{10}{10} + \dfrac{2}{10} = 1 + 0.2 = 1.2.\)

A third way is to express them as an explicit sum of an integer and a proper fraction, like this:

\(\displaystyle \dfrac{6}{5} = \dfrac{5}{5} + \dfrac{1}{5} = 1 + \dfrac{1}{5}.\)

I hope this answers your question.

PS There is nothing wrong in converting to hours, but it does add a little extra work and so a little extra opportunity for error.

 

[Bob Brown MSEE]

on representing fractions

sorry really embarrassing but does this make sense

3x1 = 3
.5 x 5 = 2.5

= 6/5
=1 1/5
not sure what thats called making it a proper fraction from improper?
what about the 3/2.5 to 6/5 is that called making it equivalent fraction?

Don't be embarrassed, there's a lot of math terminology that we take for granted. Asking questions and nailing down these terms -- is a characteristic of a good student!

--------------
6/5 = improper fraction (because 6>5)
1 1/5 = mixed fraction (the most common way to resolve an improper fraction.)
1+1/5 = how to write a mixed fraction when used in a math problem
--------------
note: improper does not mean incorrect, unless teacher says to leave the answer as a mixed fraction.

One last bit of nit-picking that you may encounter.
3/2.5 = ratio (not a fraction)
a/b = fraction when a is an integer, and b is a natural number (whole number > 0)
6/5 = fraction (improper)

The above is called nit-picking because what I said usually applies to representing a (rational) number. It is common to see the ratio of math expressions called a fraction.
3/(x+0.5) is called a fraction.

 

[lookagain]

three men paint half of a house in 1 day. How long will it take 5 men to paint whole house?

what i tried to do

three men paint whole house in 48 hours


1 man paints whole house (48 hours)*3 = 144 hours


5 men paint whole house 5/144 = 28.8 . . . No, 144/5 = 28.8, but to be consistent to the step
immediately above, (144 hours)/5 = 28.8 hours.

.

 

[bronx.system]

Thanks all everything makes sense now much appreciated
saving thread ^^