# ratio simplification

• Feb 8th 2007, 09:40 PM
elfen_lied
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:confused:

EDIT:and i need help on this problem to it makes no sense:confused: 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.
• Feb 8th 2007, 10:46 PM
ticbol
Quote:

Originally Posted by elfen_lied
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:confused:

EDIT:and i need help on this problem to it makes no sense:confused: 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 oz:oz,
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,

If you divide 2592 by 144 on your calculator, you'd get 18. :-)
• Feb 8th 2007, 11:05 PM
elfen_lied
Quote:

Originally Posted by ticbol
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 :D but what about the word problem one that one confuses me the most:confused:
• Feb 8th 2007, 11:19 PM
elfen_lied
Quote:

Originally Posted by ticbol
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 oz:oz,
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,

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
• Feb 8th 2007, 11:36 PM
ticbol
Quote:

Originally Posted by elfen_lied
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