Comparing Rates
To compare two different rates in 6th grade, convert each to a unit rate by dividing the numerator by the denominator, then compare. Store A selling 10 pens for 2.00 dollars has a unit price of 0.20 dollars per pen; Store B selling 12 pens for 3.00 dollars has 0.25 dollars per pen — Store A is the better buy. A train going 210 miles in 3 hours travels at 70 mph versus a bus at 130 miles in 2 hours traveling at 65 mph. This skill from Reveal Math, Course 1, Module 1 is essential for consumer math and rate comparisons throughout 6th grade.
Key Concepts
When two competing rates are given, it is difficult to determine which is higher or lower because they have completely different numbers. You must convert both rates to a unit rate (a rate with a denominator of 1) to make a fair comparison. This is the ultimate tool for finding the "better buy" or determining the fastest speed.
Common Questions
How do I compare two rates to find the better deal?
Convert both rates to unit rates by dividing each numerator by its denominator. Then compare the unit rates directly. The lower unit price is the better buy.
What is a unit rate and why is it useful for comparing?
A unit rate expresses a quantity per one unit (like dollars per pen or miles per hour). Converting to unit rates creates a common basis for direct comparison.
Store A has 8 pens for 2.40 dollars and Store B has 6 pens for 2.10 dollars. Which is cheaper per pen?
Store A: 2.40 divided by 8 = 0.30 per pen. Store B: 2.10 divided by 6 = 0.35 per pen. Store A is cheaper.
How do I compare two speeds using unit rates?
Divide each distance by its time to get miles per hour. The higher number is the faster speed.
When is it necessary to convert to a unit rate vs. just comparing the given ratios?
You must convert to unit rates when the quantities in the ratios are different (like 10 pens vs. 12 pens). Different denominators make direct comparison impossible without finding a common basis.
When do 6th graders learn to compare rates?
Module 1 of Reveal Math, Course 1 covers comparing rates in the Ratios and Rates unit.