Justin and Desiree each wrote a ratio comparing the numbers of students and tables in their classroom. There are 6 tables in the room with 4 students at each table.

Question

Justin states that the ratio is 4:1.
Desiree insists the ratio is 24:6.

They both ask Luke to tell them which ratio is correct. Which statement below would be the best answer for Luke?
Justin is correct because there are 4 students per table. A ratio is not correct unless it uses the smallest possible numbers.
Desiree is correct because there are 24 students to 6 tables in the room. A ratio must account for the total number of each value.
Both are correct. Desiree’s ratio compares the total number of students in the room to the total number of tables, while Justin’s is equivalent but simplified to students per table.
Neither is correct because they should have 4:6 or 2:3 for the 4 students and 6 tables.

Answer 1

The best answer for Luke would be:

Both are correct. Desiree’s ratio compares the total number of students in the room to the total number of tables, while Justin’s is equivalent but simplified to students per table.

Here’s why:

• Justin's ratio of 4:1 represents the number of students per table (with 4 students at each of the 6 tables, it can be viewed as 4 students for every 1 table).
• Desiree's ratio of 24:6 compares the total number of students (24 students total, since there are 6 tables with 4 students each) to the total number of tables.

Both ratios effectively communicate the relationship between the number of students and tables, just in different forms, and they are equivalent.