Is the teacher-to-student ratio in your school proportional to the one in my school?

Question

Homi · Accepted Answer

To check if two ratios are proportional, we must simplify each ratio to its simplest form and then compare them.

Step 1 — Simplify the given school's ratio

Let us find the teacher-to-student ratio for the given school. The ratio is the number of teachers to the number of students.

$\text{Given school's ratio} = \text{Teachers} : \text{Students}$

$= 5 : 170$

To simplify this ratio, we divide both numbers by their greatest common factor, which is 5.

$= (5 \div 5) : (170 \div 5)$

$\boxed{1 : 34}$

Diagram 1

Step 2 — Simplify my school's ratio

Now, let us find the teacher-to-student ratio for my school. The ratio is the number of teachers to the number of students.

$\text{My school's ratio} = \text{Teachers} : \text{Students}$

$= 1 : 30$

This ratio is already in its simplest form because 1 and 30 have no common factors other than 1.

$\boxed{1 : 30}$

Step 3 — Compare the ratios

We compare the simplified ratio of the given school with the simplified ratio of my school. The given school's ratio is $1 : 34$ . My school's ratio is $1 : 30$ .

These two ratios are not the same. Therefore, the teacher-to-student ratio in my school is not proportional to the one in the given school.

Answer

The given school's ratio: Teachers : Students = 1 : 34

My school's ratio: Teachers : Students = 1 : 30

These are not the same.

Question 5

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