Study on the flySHSATMathematicsRatios, unit rates, and proportional relationships
Mathematics
A ratio compares two quantities, and a unit rate expresses one quantity per single unit of another, such as miles per hour or dollars per pound.
Problems on ratios, unit rates, and proportional relationships often hide a step. When a ratio of boys to girls is given along with the difference between the groups, that difference matches a certain number of ratio parts, which sets the size of one part.
Rate problems with two machines or workers add their separate rates over the same time span. Unit conversions belong here too, especially between meters, kilometers, and centimeters, where mixing units is an easy mistake.
Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.
Question 1Easier
Machine A packs 3 crates every 4 minutes. Machine B packs 5 crates every 6 minutes. If both machines work for 24 minutes, how many crates do they pack in all?
Answer: C — 38
Machine A works for groups of 4 minutes, so it packs crates. Machine B works for groups of 6 minutes, so it packs crates. Together they pack 38 crates.
Question 2Mid
The ratio of fiction books to nonfiction books donated to a library is . If 18 more fiction books than nonfiction books are donated, how many books are donated in all?
Answer: B — 72
The difference of 2 ratio parts equals 18 books, so each part equals 9 books. The total is parts, and books.
Question 3Mid
A cable is 2.75 kilometers long. A section measuring 850 meters is removed. Each kilometer contains 1,000 meters, and each meter contains 100 centimeters. How many centimeters of cable remain?
Answer: C — 190,000 centimeters
The cable begins at meters, so meters remain, or 190,000 centimeters.
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