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chungerforever

  • 2 years ago

Please help! How would I solve 12 5/8 + 9 2/3?? Thank you!

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  1. theEric
    • 2 years ago
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    Hi! Well, adding 12 and 9 are easy. Adding those fractions is a little trickier. Would you agree that \[12\frac{5}{8} + 9\frac{2}{3}\] is the same as\[12+\frac{5}{8} +9+\frac{2}{3}\]?

  2. chungerforever
    • 2 years ago
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    yes, I would

  3. theEric
    • 2 years ago
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    Alright, and it is also the same as \[12+9+\frac{5}{8}+\frac{2}{3}\]right?

  4. theEric
    • 2 years ago
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    So 12+9, piece of cake. I can count it on my fingers (and I need some friend's fingers too). Anyway... Both fractions have to have the same bottom part, called the "denominator" if you care to remember.\[\frac{numerator}{denominator}\]

  5. theEric
    • 2 years ago
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    Lets look at JUST \[\frac{5}{8}+\frac{2}{3}\]

  6. chungerforever
    • 2 years ago
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    alright! (:

  7. theEric
    • 2 years ago
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    Now, five-eighths can't just be added to two-thirds. You have some fractions of 8 and some fractions of 3. And since an eighth is different from a third, you can just add the top numbers.

  8. theEric
    • 2 years ago
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    You have to have two fractions with the same bottom number. So they're both fractions of 24, or whatever. If you have some pieces of 24 and some other pieces of 24, you can easily know how many pieces (of 24) you have!

  9. theEric
    • 2 years ago
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    So make the bottom numbers the same with simple algebra!

  10. chungerforever
    • 2 years ago
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    so 15/24 + 16/24?

  11. theEric
    • 2 years ago
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    Say we did want to make \[\frac{5}{8}\] a fraction of 24. Here's what we'd do: Multiply 5/8 by 1. It's the only way were not actually changing it. But that doesn't look helpful. But we can't change it. Here's the trick:\[1=\frac{1}{1}=\frac{2}{2}=\frac{3}{3}=\frac{9999}{9999}\]

  12. theEric
    • 2 years ago
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    \[\frac{5}{8}*1=\frac{5}{8}*\frac{3}{3}=\frac{5*3}{8*3}=\frac{15}{24}\]

  13. theEric
    • 2 years ago
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    You see how that helps? \[\frac{2}{3}*1=\frac{2}{3}*\frac{8}{8}=\frac{2*8}{3*8}=\frac{16}{24}\]

  14. theEric
    • 2 years ago
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    Now its easier too add.

  15. chungerforever
    • 2 years ago
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    So 21 31/24?

  16. theEric
    • 2 years ago
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    Yep, but 31/24 doesn't look good. What else can it be?

  17. chungerforever
    • 2 years ago
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    reduce it?

  18. theEric
    • 2 years ago
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    Yeah! Wll, if by reduce it you mean turn it into a compound number and then make the numbers whole but as close to 0 as possible.. I don't remember big words like "reduce" :P Sorry!

  19. theEric
    • 2 years ago
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    Go ahead and show me what you get, if you want. Or we can work it out together.

  20. chungerforever
    • 2 years ago
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    Yeah I have no idea what a compound number is...

  21. theEric
    • 2 years ago
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    Oh! That's one I remember! Repeat usage, I guess. It's just a number that has a whole number and a fraction. I think\[21\frac{31}{24}\] actually counts, but I know it's not a simple-looking as it can be!

  22. theEric
    • 2 years ago
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    Another example is like\[5\frac{3}{4}\]

  23. theEric
    • 2 years ago
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    31/24 is greater than 1, so it can be a whole number plus a fraction.

  24. theEric
    • 2 years ago
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    The first step in the general way to make a fraction into a compound number is to see how many whole numbers you have. That's \[31\div24\] but not including the remainder (remainder is whatever is left over). The remainder will be written as a fraction. I know 24 goes into 31 only once. But a calculator will back me up: \[31\div24=1.2916666666666666667\]

  25. theEric
    • 2 years ago
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    So there is 1 whole number in 31/24.

  26. theEric
    • 2 years ago
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    Anyway..... After you take that "1" out of\[\frac{31}{24}\]it's \[\frac{31}{24}-1=\frac{31}{24}-\frac{24}{24}=\frac{31-24}{24}=\frac{7}{24}\]

  27. theEric
    • 2 years ago
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    \[21+\frac{31}{24}=21+1+\frac{7}{24}=22+\frac{7}{24}=22\frac{7}{24}\]

  28. theEric
    • 2 years ago
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    So you started with\[\frac{5}{8}\]and\[\frac{2}{3}\] I seemed to just randomly choose "24" as the denominator for them both, and I also seemed to just randomly choose how to multiply each fraction. But really, I multiplied each fraction by the other's denominator over itself. \[\frac{5*2}{8*3}=\frac{15}{24}\]and\[\frac{2*8}{3*8}=\frac{16}{24}\] so the "24" kinda just happened.

  29. theEric
    • 2 years ago
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    I hope I've helped more than I've hurt! I feel like my response has been jumpled, so I'm sorry. Ask me any questions you have, and I'll try to be more clear.

  30. chungerforever
    • 2 years ago
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    thank you so much!

  31. theEric
    • 2 years ago
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    You're welcome. I hope you can do the problem on your own now!

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