Finding Unit Rates Using Ratio Tables
A ratio table organizes equivalent rates visually and can be used to find a unit rate by dividing both quantities by the denominator value until the second quantity equals 1. For 120 miles in 3 hours: divide both by 3 to get 40 miles per 1 hour. For 45 pages in 5 days: divide both by 5 to get 9 pages per day. This approach from Reveal Math, Course 1, Module 1 gives 6th graders a structured visual method before they learn the direct division shortcut for unit rates.
Key Concepts
A ratio table is a visual tool used to organize equivalent rates. To find a unit rate using a ratio table, divide both quantities in the given rate by the value of the second quantity. This scales the rate down so that the second quantity becomes exactly 1.
$$\text{Rate} = \frac{a}{b} \xrightarrow{\div b} \frac{a \div b}{b \div b} = \frac{c}{1} \text{ (Unit Rate)}$$.
Common Questions
How do I use a ratio table to find a unit rate?
Write the given rate in the table. Divide both quantities by the same number until the second quantity equals 1. The first quantity in the last column is the unit rate.
What is a ratio table?
A ratio table is a visual tool that organizes equivalent rates in rows or columns. You scale rates up or down by multiplying or dividing both quantities by the same number.
Find the unit rate for 120 miles in 3 hours using a ratio table.
Divide both by 3: 120 divided by 3 = 40 miles, 3 divided by 3 = 1 hour. Unit rate = 40 miles per hour.
Find the unit rate for 45 pages in 5 days.
Divide both by 5: 45 divided by 5 = 9 pages, 5 divided by 5 = 1 day. Unit rate = 9 pages per day.
When should I use a ratio table instead of direct division for unit rates?
A ratio table is helpful when you want a visual record of your steps or when the numbers require intermediate scaling before reaching the unit rate.
When do 6th graders use ratio tables for unit rates?
Module 1 of Reveal Math, Course 1 introduces ratio tables for unit rates in the Ratios and Rates unit.