What is the purpose of a two- or three-column table in ratio problems?

• A. To display equivalent part-to-part and part-to-whole ratios
• B. To memorize multiplication tables
• C. To list prime factors
• D. To plot coordinates

Answer: (A)

Two- or three-column tables in ratio problems are used to organize how parts relate to each other and to the whole. They show the same relationship in different but equivalent forms: part-to-part, which compares one part to another, and part-to-whole, which compares a part to the total amount.

For example, if there are 2 boys and 3 girls, the table can display the ratio of boys to girls as 2:3 and the part-to-total ratios as 2:5 and 3:5. This layout makes it easy to see that if you double both parts, you get 4:6 with a total of 10, and the corresponding part-to-total ratios become 4:10 and 6:10. The table helps you spot these connections and use them to solve for unknowns or check proportionality.

Other options—like memorizing multiplication tables, listing prime factors, or plotting coordinates—serve different purposes and don’t organize the part-and-whole relationships in a way that highlights equivalent ratios.