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

1. ## 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

2. Why not convert to decimal? Otherwise the easiest thing to do would be to multiply everything by $\frac{12}{12}\cdot\frac{10.5}{10.5}$.

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

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

therefore, in one hour, the net amount filled in is $\frac{83}{84}$ of capacity of the tank.
to fulfill the tank, the time required should be $\frac{84}{83}$ hour or 1 hour 0 minute 43 seconds

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:

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

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

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

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

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

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

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

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

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

simplify:

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

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.

5. 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.

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.
$\frac{83}{84}$ is not the final answer...
It means all the three pipes together can fill up $\frac{83}{84}$, 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.

$\frac{83}{84}$ is speed, %capacity per hour, and T is time (hour). The objective is 100%, so
$\frac{83}{84}$ x T = 100% = 1
Therefore you have T = $\frac{84}{83}$
= 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