Setting up proportions upside down
210 miles in 3.5 hours; how far in 5? Write the ratio upside down and cross-multiplication confidently outputs nonsense.
Why it happens
Proportions require consistent placement (miles over hours on BOTH sides). Nothing in the mechanics warns you when one side is flipped.
See the trap
A car covers 210 miles in 3.5 hours. At that rate, how far in 5 hours?
210/3.5 = 5/x → x ≈ 0.083 miles.
210/3.5 = x/5 → x = 300 miles.
How to actually fix it
- 1Label units in the fractions: miles/hours = miles/hours.
- 2Bigger time must give bigger distance — check direction before solving.
- 3Or compute the unit rate first (60 mph), then multiply.
Practice this trap · 3 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
Absurd answers like 0.083 miles — why didn't I notice?
Cross-multiplication feels authoritative, so the result skips the plausibility check. Build the 'does the magnitude make sense?' pause into every ratio problem.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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