Rates and Fractions

Date: 1/23/96 at 21:4:46
From: Anonymous
Subject: ratios

Find out each rate as a fraction in simplest form.

1. 24 laps in 12 minutes 
2. 180 miles with 15 gallons
3. $6 for 24 ounces
4. 25 heartbeats in 10 seconds

        solve these proportions
1. 9/4 = x/28
2. 5/x = 15/24
3. 3/20 = 6/x

Date: 6/13/96 at 20:38:5
From: Doctor Lisa
Subject: Re: ratios

Hi!

Let's first deal with the first 4 questions you have that involve 
reducing each rate to simplest form.  First, rewrite the the words 
into a fraction. In number 1, this would be 24 laps/12 minutes.  
I would next see what number I can divide into both top and bottom 
of the fraction. In this case, you can divide 12 into both top and 
bottom. That would make the fraction 2 laps/1 minute. 

This should help you deal with the other 3 problems you listed.

With the second set of questions, you will use the cross-products 
property of proportions.  If you have a proportion that looks like 
a/b = c/d, then a*d = b*c.  So in the first problem you gave, 
9/4 = x/28, 9*28 = 4*x.9*28 = 252.  So 252 = 4*x.  

To get x by itself you must divide both sides by 4.  252/4 = 63.  
So 63 = x.  I hope this will help you answer the other 2 problems.

-Doctor Lisa,  The Math Forum