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Math Help - ratio simplification

  1. #1
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    ratio simplification

    how do i simplify these ratios?

    55:33



    4hours:45minutes




    13oz:2lb



    2kg:90g


    for some reason i cant find any way to simplify those


    EDIT:and i need help on this problem to it makes no sense this HW was suppose to be easy but its not since its super confusing and heres the question

    The student teacher ratio in a school with 2592 students and 144 teachers.
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  2. #2
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    Quote Originally Posted by elfen_lied View Post
    how do i simplify these ratios?

    55:33



    4hours:45minutes




    13oz:2lb



    2kg:90g


    for some reason i cant find any way to simplify those


    EDIT:and i need help on this problem to it makes no sense this HW was suppose to be easy but its not since its super confusing and heres the question

    The student teacher ratio in a school with 2592 students and 144 teachers.
    Ratio is another form of division, or another form of fraction.
    "x:y" may mean "x divided by y" or "x/y".

    So,
    55:33 = 55/33
    Just by looking at it, we can see "11" in both 55 and 33, get out the elevens to simplify the ratio.
    55:33 = 55/33 = 5(11) / 3(11) = 5/3 = 5:3 ----------simplified form.

    -----------------
    4hrs : 45 minutes
    = 4hrs / 45 min

    Put both numerator and denominator in the same units. hrs:hrs, or min:min.

    In hrs:hrs,
    = 4hrs / (45/60)hr
    = 4 / (3/4)
    = 4*(4/3)
    = 16/3
    = 16:3 -------------------simplified form.

    In min:min,
    = 4*60 / 45
    = 240/45
    = 48/9
    = 16/3
    = 16:3 ---------same.

    ---------------------------------------------------

    Wait. I accidentally pressed the "Submit" button. :-)

    --------------------
    13oz : 2lbs

    What is the conversion of 1 lb to oz?
    Say, 1 lb = 16 oz, so:

    In ozz,
    13oz : 2lbs
    = 13oz / (2*16)oz
    = 13/32
    = 13:32 ----------simplified form

    In lbs:lbs,
    = (13/16)lbs / 2lbs
    = (13/16)*(1/2)
    = 13/32
    = 13:32 ------------same.

    --------------------------------------------
    2kg = 90grams

    In kg:kg,
    2kg : 90grams
    = 2kg / (90/1000)kg
    = 2*(1000/90)
    = 2000/90
    = 200/9
    = 200:9

    In grams:grams,
    = (2*1000)grams / 90grams
    = 2000/90
    = 200:9 ------------same.

    -----------------------------------------------------
    The student teacher ratio in a school with 2592 students and 144 teachers.
    s:t = 2592:144
    = 2592/144
    = 1296/72
    = 648/36
    = 324/18
    = 162/9
    = 54/3
    = 18/1
    Hence,
    student:teacher = 18:1 ------------answer.

    If you divide 2592 by 144 on your calculator, you'd get 18. :-)
    Last edited by ticbol; February 8th 2007 at 11:07 PM.
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  3. #3
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    Quote Originally Posted by ticbol View Post
    Ratio is another form of division, or another form of fraction.
    "x:y" may mean "x divided by y" or "x/y".

    So,
    55:33 = 55/33
    Just by looking at it, we can see "11" in both 55 and 33, get out the elevens to simplify the ratio.
    55:33 = 55/33 = 5(11) / 3(11) = 5/3 = 5:3 ----------simplified form.

    -----------------
    4hrs : 45 minutes
    = 4hrs / 45 min

    Put both numerator and denominator in the same units. hrs:hrs, or min:min.

    In hrs:hrs,
    = 4hrs / (45/60)hr
    = 4 / (3/4)
    = 4*(4/3)
    = 16/3
    = 16:3 -------------------simplified form.

    In min:min,
    = 4*60 / 45
    = 240/45
    = 48/9
    = 16/3
    = 16:3 ---------same.

    ---------------------------------------------------

    Wait. I accidentally pressed the "Submit" button. :-)

    thanks but what about the word problem one that one confuses me the most
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  4. #4
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    Joined
    Oct 2006
    Posts
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    Quote Originally Posted by ticbol View Post
    Ratio is another form of division, or another form of fraction.
    "x:y" may mean "x divided by y" or "x/y".

    So,
    55:33 = 55/33
    Just by looking at it, we can see "11" in both 55 and 33, get out the elevens to simplify the ratio.
    55:33 = 55/33 = 5(11) / 3(11) = 5/3 = 5:3 ----------simplified form.

    -----------------
    4hrs : 45 minutes
    = 4hrs / 45 min

    Put both numerator and denominator in the same units. hrs:hrs, or min:min.

    In hrs:hrs,
    = 4hrs / (45/60)hr
    = 4 / (3/4)
    = 4*(4/3)
    = 16/3
    = 16:3 -------------------simplified form.

    In min:min,
    = 4*60 / 45
    = 240/45
    = 48/9
    = 16/3
    = 16:3 ---------same.

    ---------------------------------------------------

    Wait. I accidentally pressed the "Submit" button. :-)

    --------------------
    13oz : 2lbs

    What is the conversion of 1 lb to oz?
    Say, 1 lb = 16 oz, so:

    In ozz,
    13oz : 2lbs
    = 13oz / (2*16)oz
    = 13/32
    = 13:32 ----------simplified form

    In lbs:lbs,
    = (13/16)lbs / 2lbs
    = (13/16)*(1/2)
    = 13/32
    = 13:32 ------------same.

    --------------------------------------------
    2kg = 90grams

    In kg:kg,
    2kg : 90grams
    = 2kg / (90/1000)kg
    = 2*(1000/90)
    = 2000/90
    = 200/9
    = 200:9

    In grams:grams,
    = (2*1000)grams / 90grams
    = 2000/90
    = 200:9 ------------same.

    -----------------------------------------------------
    The student teacher ratio in a school with 2592 students and 144 teachers.
    s:t = 2592:144
    = 2592/144
    = 1296/72
    = 648/36
    = 324/18
    = 162/9
    = 54/3
    = 18/1
    Hence,
    student:teacher = 18:1 ------------answer.

    If you divide 2592 by 144 on your calculator, you'd get 18. :-)

    thanks thanks thanks ALOT! oh and how do i do this proportion problem?

    18x/13=36/39
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  5. #5
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    Quote Originally Posted by elfen_lied View Post
    thanks thanks thanks ALOT! oh and how do i do this proportion problem?

    18x/13=36/39
    Ah, that's another problem. It is one ratio equal to another ratio.

    One short cut, or popular way, in doing that is by cross multiplication.
    Multiply the numerator of one to the denominator of the other, and vice versa. Or, multiply also the denominator of the "one" to the numerator of the "other". Then equate those.

    Words!

    It is simply like this:
    18x /13 = 36 /39
    Cross multiply,
    18x *39 = 13*36
    Divide both sides by 18,
    x*39 = 13*2
    Divide both sides by 13,
    x*3 = 2
    x = 2/3 -----------------------answer.

    ----------------------------
    Another way is by clearing all fractions. Like so:

    18x /13 = 36 /39
    Clear the fractions, multiply both sides by 39
    18x *3 = 36
    x = 36/(18*3)
    x = 2/3 ------------------answer.
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