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jewjewbri

  • 3 years ago

Perform the indicated operation. 9/32-1/16 I did the math: 9*16/32*16 - 1*32/32*16 = 144/512 - 32/512 = 112/512 How would I simplify this?

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  1. theEric
    • 3 years ago
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    I would recommend that you start like so: \[\frac{9}{32}-\frac{1}{16}=\]\[\frac{9}{32}-\frac{1*2}{16*2}=\] \[\frac{9}{32}-\frac{2}{32}= \frac{7}{32}\]

  2. theEric
    • 3 years ago
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    However, \[\frac{112}{512}\]is also correct, and we can simplify it so you know how for another time!

  3. jewjewbri
    • 3 years ago
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    Oh ok, that would be great if you could help with that. Im lost with that big of a number

  4. theEric
    • 3 years ago
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    Okay! The quickest way is to divide by the "greatest common factor". But then you have to know the greatest common factor. So instead, I divide top and bottom by prime numbers to get whole numbers on top and bottom until I can't anymore!

  5. theEric
    • 3 years ago
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    I divide top and bottom by two until I get a decimal from one.

  6. jewjewbri
    • 3 years ago
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    So divide them by 2 until the smallest number can't divide down?

  7. theEric
    • 3 years ago
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    \[\frac{112}{512}=\frac{112\div2}{512\div2}=\frac{56}{256}\]

  8. theEric
    • 3 years ago
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    Yep! Keep on dividing down.

  9. jewjewbri
    • 3 years ago
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    Oh, I kept dividing till I got 1/2

  10. jewjewbri
    • 3 years ago
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    But the answers are: 1/4. 5/16. and 7/32

  11. theEric
    • 3 years ago
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    \[\frac{56\div2}{256\div2}=\frac{28}{128}\]

  12. theEric
    • 3 years ago
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    \[\frac{28\div2}{128\div2}=\frac{14}{64}\]

  13. jewjewbri
    • 3 years ago
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    oh so just divide by 2 one more time?

  14. theEric
    • 3 years ago
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    \[\frac{14\div2}{64\div2}=\frac{7}{32}\]

  15. theEric
    • 3 years ago
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    7 is a prime number, so it can't be divided by anything but itself to get a whole number. So you could divide top and bottom by 7, but 7 doesn't go evenly into 32, so you're left with \[\frac{7}{32}\]

  16. theEric
    • 3 years ago
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    The trick is dividing by prime numbers as long as you can.

  17. theEric
    • 3 years ago
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    Once you hit a prime number, you know it can be divided only by itself. Once a prime number is on the bottom, you're done (unless you divide the bottom by itself, and then you don't have a fraction). For the top, just keep trying to divide by prime numbers until there are no prime numbers left that are smaller than the number on top.

  18. theEric
    • 3 years ago
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    Thanks! Take care! Ask any follow-up questions here and I'll look for them later! Lists of prime numbers are on the internet!

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