Ratios & Rates
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Lesson overview
Comparing quantities and unit rates in word problems.
Go to lesson quiz →Exam guidance · GED Reasoning & Formula-Sheet Lens
Pacing
~2–2.5 minutes per item with an on-screen calculator and official formula sheet.
How GED marks this
Translating word scenarios, charts, and tables into equations rather than rote formula memorisation.
Watch out for
Answering the wrong target quantity (e.g., solving for x when the prompt asks for 2x + 5 or percentage change).
Lesson content
Overview — Ratios & Rates
Comparing quantities and unit rates in word problems. This lesson is at the beginner level — by the end, you'll be able to recognise this question type, apply a reliable method, and avoid the traps that cost marks.
Key Concept
A ratio compares two quantities directly (3 apples to 2 oranges), while a rate compares two quantities with different units (miles per hour, dollars per pound), and a unit rate simplifies that comparison to a single unit (one hour, one pound).
Why It's Tested This Way
The GED tests ratios and rates because comparing prices, speeds, and quantities using unit rates is one of the most common real-world math tasks adults perform, from grocery shopping to planning a trip.
Method
To find a unit rate, divide the first quantity by the second so the second quantity becomes 1 (e.g., total cost ÷ total pounds = cost per pound), and to compare two options, convert both to the same unit rate before comparing.
Worked Example
A 12-ounce box of cereal costs $3.60 and an 18-ounce box costs $5.04. Unit prices are 3.60/12 = $0.30/oz and 5.04/18 = $0.28/oz — the larger box is the better deal despite costing more overall.
Second Worked Example
A car travels 180 miles in 3 hours; find its rate in miles per hour. Unit rate = 180/3 = 60 miles per hour, which can then be used to find the time for any other distance at the same speed.
Common Traps
The trap is comparing two quantities without first converting to the same unit basis (comparing total price instead of price-per-unit) — always reduce to a single, comparable unit rate before deciding which option is better.
Lesson Summary
Remember: (1) identify what is being asked, (2) apply the GED strategy, (3) check against the traps. Complete the 10-question quiz below to unlock the next lesson — you need at least 60% to pass.
Mastery Check · Lesson Quiz · pass 60%
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