Math 6 Honors ( Periods 1, 2, & 3)

Proportions 7-7
We used fictional numbers for the middle schools in our district
AEWright 6th grade 160 students and 10 teachers
ACStelle 6th grade 144 students and 9 teachers
We looked at the teacher to student ratios of both schools and found
10/160 = 1/16
and
9/144 = 1/16

so 10/160 = 9/144
An equation that states two ratios are equal is called a proportion
10, 160, 9, and 144 are called the terms of the proportion.
Let's say LCMS has 192 students. How many teachers will be needed if the teacher- strudent ratio needs to be the same?

Let t = the number of teachers
10/160 = t/192

Using cross multiplying we discovered that
160t = 192 (10)

160t = 192 (10)
160 160

t = 192/16
or t = 12

12 teachers

we found that when
a/b = c/d and b is not equal to 0 and d is not equal to zero
then
ad = bc


3/8 = 12/n
3n = 8 (12)
3n = 96
3n/3 = 96/3
n = 32

what about 4/3 = n/7
3n = 4(7)
3n = 28

3n/3 = 28/3

n = 9 1/3

3/75 = 2/n
n = 50

3/m = m/27
m² = 3 (27)
m² = 81
so m = 9

49/n = n/4
n² = 4(49)
n² = 196
n = 14