The key idea
Multiply by conversion factors written as fractions equal to 1, arranged so the units you don't want cancel. For areas and volumes, square or cube the length conversion.
The trap
Converting square feet to square yards by dividing by 3 instead of 9.
Can Desmos do it?
Desmos will multiply anything you type. Setting up which factor goes on top is the part that earns the point.
College Board skill: Ratios, rates, proportional relationships, and units · Problem-Solving and Data Analysis
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
A cyclist rides at a constant speed of 138 kilometers per hour. What is this speed in meters per second?
Show the answer
Answer: 115/31 h138 km⋅1 km1,000 m⋅3,600 s1 h=3115 meters per second.
Level 2 · Test level
Carpet costs $36 per square yard. How much would it cost, in dollars, to carpet a rectangular room that is 12 feet long and 9 feet wide? (1 yard = 3 feet)
Show the answer
Answer: 432The room is 312=4 yards by 39=3 yards, or 12 square yards. (Equivalently, 108 square feet divided by 9.) The cost is 12×36=432 dollars.
Level 3 · Beyond the test
A leaky faucet drips 1 drop every 4 seconds, and 20 drops make 1 milliliter. How many liters of water does the faucet drip in one week?
Show the answer
Answer: 7.56A week has 7×24×3,600=604,800 seconds, which is 4604,800=151,200 drops, or 20151,200=7560 milliliters. Divide by 1,000: 7.56 liters.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
Percent change, chained and reversedChained and reversed percent changes, and the right base.36 questions, 3 levelsMixtures and concentrationConcentration problems: mixing, adding water, draining and replacing.36 questions, 3 levelsWork ratesJobs done together, fill-and-drain, and late starts.36 questions, 3 levelsMeans, medians, and changes to dataTotals, combined groups and the score you need next.36 questions, 3 levelsConditional probability“Given that” from tables and percents.36 questions, 3 levelsRatios and proportionsRatios that change when one part changes.36 questions, 3 levels