Skill: Interpret ratios in context

A ratio compares quantities by saying how much of one quantity there is for a given amount of another. The order matters.

Worked example

In a class, 8 students choose soccer and 4 students choose basketball.

1. Identify the quantities and their units.

• Soccer: $8$ students
• Basketball: $4$ students
• Total students: $(8+4=12)$ students

2. Write the ratio in the requested order.

The ratio of soccer students to basketball students is

$$8:4$$

This means for every 8 soccer students, there are 4 basketball students.

3. Simplify the ratio if possible.

Both numbers can be divided by $4$:

$$8:4=2:1$$

So the relationship can also be described as 2 soccer students for every 1 basketball student. The ratios $(8:4)$ and $(2:1)$ describe the same relationship.

4. Notice the difference between part-to-part and part-to-whole.

• Soccer to basketball is a part-to-part ratio:

$$8:4=2:1$$

• Soccer to all students is a part-to-whole ratio. Since there are $(12)$ students total:

$$8:12=2:3$$

This means 2 out of every 3 students are soccer students.

Always check the order and label what each number represents. For example, $(4:8)$ would mean basketball to soccer, not soccer to basketball.