# How do you add fractions, with decimals in them. CONFUSED big time.

• Nov 21st 2009, 09:00 AM
How do you add fractions, with decimals in them. CONFUSED big time.
Ok here is Q#1
A tank can be filled by one of two pipes in 12.00 h and by the other of the two in 1.00 h. The same tank can be emptied by a drain pipe in 10.5h. If all three pipes are open, how long will it take to fill the tank.

I know it's 1/12 + 1/1 - 1/10.5 = Need to find the time it takes to fill the tank.

I have no clue on subtracing a fraction with a decimal if you have to have the LCD to clear the fractions???

Joanne
• Nov 21st 2009, 09:41 AM
lvleph
Why not convert to decimal? Otherwise the easiest thing to do would be to multiply everything by $\displaystyle \frac{12}{12}\cdot\frac{10.5}{10.5}$.
• Nov 21st 2009, 10:04 AM
ukorov
Quote:

Ok here is Q#1
A tank can be filled by one of two pipes in 12.00 h and by the other of the two in 1.00 h. The same tank can be emptied by a drain pipe in 10.5h. If all three pipes are open, how long will it take to fill the tank.

I know it's 1/12 + 1/1 - 1/10.5 = Need to find the time it takes to fill the tank.

I have no clue on subtracing a fraction with a decimal if you have to have the LCD to clear the fractions???

Joanne

$\displaystyle \frac{1 * 2}{10.5 * 2}$ = $\displaystyle \frac{2}{21}$ and the LCM of 12 and 21 = 84
so you have $\displaystyle \frac{7}{84} + \frac{84}{84} - \frac{8}{84}$

therefore, in one hour, the net amount filled in is $\displaystyle \frac{83}{84}$ of capacity of the tank.
to fulfill the tank, the time required should be $\displaystyle \frac{84}{83}$ hour or 1 hour 0 minute 43 seconds
• Nov 21st 2009, 10:11 AM
aidan
Quote:

Ok here is Q#1
A tank can be filled by one of two pipes in 12.00 h and by the other of the two in 1.00 h. The same tank can be emptied by a drain pipe in 10.5h. If all three pipes are open, how long will it take to fill the tank.

I know it's 1/12 + 1/1 - 1/10.5 = Need to find the time it takes to fill the tank.

I have no clue on subtracing a fraction with a decimal if you have to have the LCD to clear the fractions???

Joanne

I look at it this way:

$\displaystyle \dfrac{1}{2} = \dfrac{2}{4} = \dfrac{4.123}{8.246}$

They are equivalent. They are NOT in lowest term, but they represent the same quantity.

Example:
$\displaystyle \dfrac{7}{11.19}+\dfrac{5}{3.38}$

To get the LCD:
$\displaystyle \left( \dfrac{7}{11.19}\times\dfrac{3.38}{3.38}\right) + \left(\dfrac{5}{3.38}\times\dfrac{11.19}{11.19}\ri ght)$

$\displaystyle \left( \dfrac{7\times 3.68}{11.19\times 3.38}\right) + \left(\dfrac{5\times 11.19}{3.38\times 11.19}\right)$

$\displaystyle \left( \dfrac{7\times 3.68 + 5\times 11.19}{3.38\times 11.19}\right)$

$\displaystyle \dfrac{1}{12} + \dfrac{1}{1} - \dfrac{1}{10.5}$

get a common denominator
$\displaystyle \left( \dfrac{1}{12}\times\dfrac{10.5}{10.5} \right)+\left( \dfrac{1}{1}\times\dfrac{12}{12}\times \dfrac{10.5}{10.5}\right) - \left(\dfrac{1}{10.5}\times\dfrac{12}{12}\right)$

$\displaystyle \dfrac{\left( 1 \times 10.5 \right)+\left( 1 \times 12 \times 10.5 \right) - \left( 1 \times 12 \right)}{12\times 10.5}$

simplify:

$\displaystyle \dfrac{(10.5 ) + (12 \times 10.5) - (12)}{12\times 10.5}$ = $\displaystyle \dfrac{ 10.5 + 12 \times 10.5 - 12 }{12\times 10.5}$

then use the calculator to get the decimal numerator & denominator, then divide.
NOTE: This is what happens in 1 hour -- not how long it is required to actually fill the tank.

.Hope that helps.
• Nov 21st 2009, 11:50 AM
So the answer is 166/168 but you invert it correct to 168/166
which equals 1.012 hours??

Do I have this right?

And to round to the nearest quarter of an hour.
.012 X 60 minutes = .72 of a minute?

I must be wrong, does not look right. Help in solving please.
• Nov 21st 2009, 07:28 PM
ukorov
Quote:

So the answer is 166/168 but you invert it correct to 168/166
which equals 1.012 hours??

Do I have this right?

And to round to the nearest quarter of an hour.
.012 X 60 minutes = .72 of a minute?

I must be wrong, does not look right. Help in solving please.

$\displaystyle \frac{83}{84}$ is not the final answer...
It means all the three pipes together can fill up $\displaystyle \frac{83}{84}$, or 98.81% of the total capacity of the tank, which means not 100%. In other words, it takes the pipes a little bit more than 1 hour to fulfill it.

$\displaystyle \frac{83}{84}$ is speed, %capacity per hour, and T is time (hour). The objective is 100%, so
$\displaystyle \frac{83}{84}$ x T = 100% = 1
Therefore you have T = $\displaystyle \frac{84}{83}$
= 1.012 (hour)
= 1 hour + (0.012 x 60) minutes
= 1 hour 0.72 minutes
= 1 hour + (0.72 x 60) seconds
= 1 hour 43 seconds