**In Ms. Matthews' classroom, there
are 12 boys and 15 girls. In Mr. Lopez's classroom, there are
8 boys and 6 girls. In Ms. Waddell's classroom, there are 4 boys
and 5 girls.**

**Which
two classrooms have the same boys-to-girl ratio?
**

Ms. Louvin's class has a boy-to-girl ratio of 5 to 6. At the end of the 1st, 2nd, and 3rd quarters, the class gets larger by two boys and one girl. So, by the end of the year, Ms. Louvin has 6 extra boys and 3 extra girls in her class since the beginning of the year. If the class never has more boys than girls, then what is Ms. Louvin's largest possible class size at the beginning of the year?

**Related External Resources**

Oranges project - Students
investigate the proportional relationship between the edible part
of an orange and the peel or inedible part of a orange.

**http://www.fi.edu/sln/school/tfi/fall96/oranges.html**

Ratio and proportion -
A lesson plan in which the students will use the phenomenological
approach to complete the activities, calculate ratios and proportions
and compare and contrast group data with class data.

**http://www.iit.edu/~smile/ma9403.html**

Does more wins mean more
fans at the ballpark? - Determine an attendance-to-win ratio for
each of the 28 major league teams and then study the results to
see if winning always leads to good attendance.

**http://score.kings.k12.ca.us/lessons/ballpark.htm**

Ratios, Mars, and the
Internet - A lesson plan in which students are involved in calculating
real ratios that exist between the planets Earth and Mars.

**http://score.kings.k12.ca.us/lessons/ratio.mars.html**

**Submit your idea for an investigation
to InterMath**

Ms. Matthews' class ratio is 12:15 (which is also eqivalent to 4:5).

Mr. Lopez's class ration is 8:6 (which is also equivalent to 4:3).

Ms. Waddell's class ratio is 4:5.

20 boys

21 girls

Looking back at the reduced ratios, Ms. Matthews had a ratio of 4:5 and Mr. Lopez had a ratio of 4:3. Now when I combined these, I had

(4+4)/(5+3) = 8:8, which reduced to a 1:1 ratio!!! Well, that cannot be because combining the original numbers actually led me to a 20:21 ratio, so it is quite obvious that the reduction did not lead to the same ratio. Simply put, the sum of reduced ratios does not ALWAYS give a correct ratio for the original number.

Let's look at this in another way using fractions. Okay, combining Ms. Matthews' and Mr. Lopez's classes, using the reduced fractions gives 8/8 or 1/1...AND...combining Ms. Matthews' and Mr. Lopez's classes, again using the reduced fractions gives 8/8 or 1/1. When you cross multiply these two, they say they are equal. Now, is this truly correct? NO! The reason is in the original combined numbers, 20/21 and 12/11. The first thing I saw is that one is a common fraction and the other is an improper fraction....dingdingding!!! and when I cross multiply these they prove they are not equal!

12 boys

11 girls

Looking back at the reduced ratios of Ms. Waddell (4:5) and Mr. Lopez (4:3), which gives me (4+4)/(5+3), again leading to an 8:8 or 1:1 ratio. However, the original numbers in the ratio were (4:5) and (8:6), respectively. Combining the classes lead to an (4+8)/(5+6) or 12:11 ratio.

According to ** Contemporary
Mathematics for elementary teachers** (1966), "ratio
was defined in terms of the measures of two segments, or of two
magnitudes with the same unit of measure. We, can however, think
of any two numbers as being possible measures, and hence define
their quotient to be a ratio...

Now, according to this statement,
this gives the reasoning why the two (Ms. Matthews' and Ms. Waddell's)
ratios **are** equal, but upon further examination, I found
that when I combined the numbers in the groups, the new ratios
could be found from the sums of those groups...i.e. you CANNOT
add reduced ratios and get correct answers.

**above**.