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Q&A #10504

Teachers' Lounge Discussion: Proportions and ratios

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From: Loyd <Loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2003120816:02:50
Subject: Re: porportions


A ratio is a fraction.

A proportion is a statement that two ratios are equal.  

Thus, 3/4 = 6/8  is two ratios that are equal.  Now if you didn't know
this fact, you could have:

3/4=x/8   and you could then solve like any equation.  If there are
only two terms, such as the above, you can just cross multiply and
get:

(3)(8)=(4)(x) or 24 = 4x and x=6.

Ratios and proportions are really great when you know something like:

30 miles per hour is exactly 44feet per second.

Knowing that fact makes it easy to find out how many miles per hour is
1100 feet per second.

30/x = 44/1100 and after cross multiplying:

30(1100) = 44x
33000=44x
x=750 miles per hour.  

Notice that the left side of the proportion is miles to miles and the
right side is feet to feet.  There are eight ways to set up this
proportion and eight ways to set up wrong.  

You need to keep the same order on both sides such as "small to large"
= "small to large";otherwise you will have an inverse proportion.  

The classic example is:  A yard stick casts a shadow 4 feet long.  How
tall is a tree that casts a shadow 40 feet long?

short vertical/tall vertical = short shadow/tall shadow

3/4 = x/40

3x=120 and x = 40

Hope this helps.



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