Question

Martha recorded the ratio of students and teachers at all the middle schools in the Timber Creek school district. The list is shown below.

20 students : 2 teachers
1 teacher per 15 students
1 teacher per 10 students
40 students : 4 teachers
5 teachers per 40 students
Part A: Identify the unit rates and ratios that are equivalent.

Part B: Give another unit rate or ratio that is not on the list but is equivalent to the ones from Part A. Explain why these are equivalent.

Answer 1

First convert each entry to the same unit (students per 1 teacher):

- 20 students : 2 teachers = 20 ÷ 2 = 10 students per teacher.
- 1 teacher per 15 students = 15 students per teacher.
- 1 teacher per 10 students = 10 students per teacher.
- 40 students : 4 teachers = 40 ÷ 4 = 10 students per teacher.
- 5 teachers per 40 students = 40 ÷ 5 = 8 students per teacher.

Part A — Equivalent ratios/unit rates:
- The equivalent ones are 20 students : 2 teachers, 1 teacher per 10 students, and 40 students : 4 teachers — each equals 10 students per 1 teacher.
- The others (1 teacher per 15 students = 15 students/teacher, and 5 teachers per 40 students = 8 students/teacher) are not equivalent to those.

Part B — Another equivalent ratio:
- Example: 30 students : 3 teachers. This equals 30 ÷ 3 = 10 students per teacher, so it is equivalent.
- Why: Equivalent ratios are multiples (or reductions) of one another. 30:3 = 10:1, the same unit rate (10 students per teacher) as 20:2 and 40:4.