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Math Help - Multiplying & Dividing Fractions - Application

  1. #1
    Junior Member Euclid Alexandria's Avatar
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    Question Multiplying & Dividing Fractions - Application

    From the book: "A special on a cruise to the Bahamas is advertised to be \frac{2}{3} of the regular price. If the regular price is $2757, what is the sale price?"

    I know I veered way off course at some point here, but I couldn't find any common factors to divide out.

    My answer:

    x = sale\ price

    x = 2,757 \div \frac{2}{3}

    = \frac{2,757}{1} \div \frac{2}{3} = \frac{2,757}{1} \cdot \frac{3}{2} = \frac{2,757 \cdot 3}{1 \cdot 2} = \frac{8,271}{2}
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Euclid Alexandria
    From the book: "A special on a cruise to the Bahamas is advertised to be \frac{2}{3} of the regular price. If the regular price is $2757, what is the sale price?"

    I know I veered way off course at some point here, but I couldn't find any common factors to divide out.

    My answer:

    x = sale\ price

    x = 2,757 \div \frac{2}{3}

    = \frac{2,757}{1} \div \frac{2}{3} = \frac{2,757}{1} \cdot \frac{3}{2} = \frac{2,757 \cdot 3}{1 \cdot 2} = \frac{8,271}{2}
    You divided by 2/3 when you should have multiplied. As a check, note that the sale price should be less than the regular price.

    sale price = $ 2757*\frac{2}{3} = \frac{5514}{3}=$1838

    -Dan
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  3. #3
    Junior Member Euclid Alexandria's Avatar
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    Thumbs up Thanks for getting me unstuck!

    Quote Originally Posted by topsquark
    As a check, note that the sale price should be less than the regular price.
    Yeah that's what tipped me off that I'd goofed up. I know the key word in the application is the word of, but at some point I started incorrectly thinking that meant "divide."
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  4. #4
    Junior Member Euclid Alexandria's Avatar
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    Question

    Here's another application using the word of, except this time, multiplying isn't seeming to work at first glance. I was expecting to end up with a whole number/dollar amount. Any hints on where I'm going wrong?

    From the book: "The Gonzales recently sold their house for $102,000, but \frac{3}{50} of this amount goes to the real estate companies that helped them sell their house. How much money do the Gonzales pay to the real estate companies?"

    My answer

    x = 102,000

    = \frac{3}{50} \cdot \frac{102,000}{1} = \frac{3 \cdot 34,000}{50 \cdot 1} = \frac{102,000}{50}
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  5. #5
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by Euclid Alexandria
    Here's another application using the word of, except this time, multiplying isn't seeming to work at first glance. I was expecting to end up with a whole number/dollar amount. Any hints on where I'm going wrong?

    From the book: "The Gonzales recently sold their house for $102,000, but \frac{3}{50} of this amount goes to the real estate companies that helped them sell their house. How much money do the Gonzales pay to the real estate companies?"

    My answer

    x = 102,000

    = \frac{3}{50} \cdot \frac{102,000}{1} = \frac{3 \cdot 34,000}{50 \cdot 1} = \frac{102,000}{50}
    You've done the work right, except that \frac{3}{50} \cdot \frac{102,000}{1} \neq \frac{3 \cdot 34,000}{50 \cdot 1} it really is  \frac{3}{50} \cdot \frac{102,000}{1} = \frac{3 \cdot 102,000}{50 \cdot 1}

    with that in mind, the rest is easy...

     \frac{3\cdot102,000}{50\cdot1}

     \frac{306,000}{50}

     6,120

    so the amount payed to the real-estate company is $6,120.
    Last edited by Quick; June 13th 2006 at 03:16 PM. Reason: just correcting a mistake
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  6. #6
    Junior Member Euclid Alexandria's Avatar
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    Angry

    Thanks.

    I either need to

    A) Get more sleep, or
    B) Drink more Monster.

    Obviously, I divided. Again. Even after inserting a multiplication symbol.
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