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Math Help - How do you add fractions, with decimals in them. CONFUSED big time.

  1. #1
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    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.

    Answer in time?
    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???

    Please help thanks - PLEASE EXPLAIN how it's calculated.
    Joanne
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  2. #2
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    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}.
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  3. #3
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    Quote Originally Posted by bradycat View Post
    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.

    Answer in time?
    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???

    Please help thanks - PLEASE EXPLAIN how it's calculated.
    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
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  4. #4
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    Quote Originally Posted by bradycat View Post
    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.

    Answer in time?
    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???

    Please help thanks - PLEASE EXPLAIN how it's calculated.
    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)



    Your specific example:

     \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.
    Last edited by aidan; November 21st 2009 at 10:17 AM. Reason: typo
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  5. #5
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    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.
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  6. #6
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    Quote Originally Posted by bradycat View Post
    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
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